## 1. Main Economic Indicators

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### I. Introduction: purpose and contribution
- Purpose: quantify the cost of financial innovation by analyzing the introduction of the Argentine GDP-indexed warrants.
- Contribution: estimate a theoretically derived "novelty premium" for the Argentine GDP-warrants by comparing model-implied prices with market prices.
- Simulation approach:
  - Simulate 5,000 paths for jointly-distributed stochastic processes for GDP, inflation, and the exchange rate; compute implied warrant payments in each path.
- Key modeling elements:
  - A discount rate and three stochastic processes (GDP, inflation, exchange rate) whose mean and volatility are based on market expectations and historical evidence.

### II. The Argentine GDP-warrants: background and issuance
- Context and aggregate quantities:
  - Stock of debt in default (end-2003): US$101.2 billion.
  - Value of debt eligible for exchange: US$81.8 billion.
  - Creditor participation: 76 percent.
  - Sum of notional amounts of all warrants (reflecting 76 percent participation): US$62bn.
  - Participating creditors swapped combined face-value of about US$62 billion for a new set of bonds with face-value of US$35.3 billion.
  - Exchange concluded on June 10, 2005.
- Currency distribution of detachable GDP-linked securities (measured in Dec. 2003 Exchange Rates; in percentage of 62bn Total*):
  - Ar$ (Arg Law): 47%
  - Euro (British Law): 24%
  - US$ (NY Law): 23%
  - US$ (Arg Law): 5%
  - Yen (Japan Law): 1%
- Rationale:
  - GDP-linked securities raised expected value of the exchange offer and acted as automatic-stabilizers by shifting payments toward favorable growth scenarios.

### III. Payment formula and contractual features
- Payment timing and mechanics:
  - Payments made on December 15 of the year following the reference year (first payment made in 2006).
  - Trades are ex-dividend starting December 12.
- Payment triggers (all three must hold for a payment to occur):
  1. actual real GDP must exceed baseline real GDP in the reference year;
  2. growth in actual real GDP must exceed growth in baseline real GDP in the reference year;
  3. cumulative past payments should not exceed 0.48 per unit of security (in its corresponding currency).
- Payment base:
  - If triggered, payment equals a fraction of excess GDP (difference between actual GDP and baseline GDP).
  - Fraction equals 3.8 percent of excess GDP (76 percent participation × 5 percent).
- Notation and key variables (as in source):
  - C(j)_{t+1}: Coupon payment at time t+1 of the warrant in currency j.
  - j: Type of currency denomination: Argentine peso, U.S. dollar, Euro, or Yen.
  - Y_t: Nominal GDP in period t, in current prices.
  - y^b_t: Real GDP in baseline case for period t.
  - D_t: GDP price deflator in period t, base 1993=1.
  - ER_t: Exchange rate in Arg$ per unit of currency j in period t.
  - U(j): Unit of currency coefficient.
  - y_t: Real GDP in period t, in 1993 prices.
  - Δ: Represents the growth rate.
  - I(.) indicator functions equal 1 when the corresponding inequality holds, and 0 otherwise.
- Important contract features emphasized:
  - Payment depends on level of real GDP relative to baseline, not directly on growth rate (growth affects payment via level).
  - Discontinuity of growth effect: payments occur only when growth exceeds a threshold (about 3 percent), producing discontinuous effects around that threshold.
  - Cap on cumulative payments: 0.48 per unit.

### IV. Key statistics and contractual quantities (reported)
- Aggregate and notional:
  - Sum of notional amounts of all warrants: US$62bn.
- Table of outstanding value, unit coefficients, and first coupon as percent of original currency outstanding value (values in units of each currency; using exchange rates by Dec 31st 2003):
  - US$ (NY Law): Outstanding value 14,386; Unit coefficient U(j) = 1/81.8; First coupon percent = 89.840.6245
  - US$ (Arg Law): Outstanding value 2,925; Unit coefficient = 1/81.8; First coupon percent = 18.270.6245
  - Euro (British Law): Outstanding value 11,808; Unit coefficient = (1/81.8)*(1/0.7945); First coupon percent = 78.150.6618
  - Ar$ (Arg Law): Outstanding value 86,154; Unit coefficient = (1/81.8)*(1/2.9175); First coupon percent = 559.220.6491
  - Yen (Japan Law): Outstanding value 38,369; Unit coefficient = (1/81.8)*(1/107.42292); First coupon percent = 261.200.6808
  - Total (In Dollars*): 62,318
  - Note: Unit of currency U(j) (for billions of currency j) defined as 1/81.8 multiplied by the inverse of the exchange rate in terms of currency j per dollar; sum of units times outstanding amounts equals US$62bn/US$81.8bn = 76 percent.
- Selected macroeconomic indicators (annual series 1999–2006, preserved exactly):
  - Real GDP (in billions of 1993 pesos): 1999: 278.4; 2000: 276.2; 2001: 264.0; 2002: 235.2; 2003: 256.0; 2004: 279.1; 2005: 304.8; 2006: 330.6
  - GDP growth (in percent): 1999: -3.4; 2000: -0.8; 2001: -4.4; 2002: -10.9; 2003: 8.8; 2004: 9.0; 2005: 9.2; 2006: 8.5
  - CPI inflation (in percent): 1999: -1.8; 2000: -0.7; 2001: -1.5; 2002: 40.9; 2003: 3.7; 2004: 6.1; 2005: 12.3; 2006: 9.8
  - Unemployment rate (in percent): 1999: 14.5; 2000: 15.4; 2001: 16.4; 2002: 21.5; 2003: 14.5; 2004: 12.1; 2005: 10.1; 2006: 8.7
  - Current Account (In billions of US$): 1999: -12.0; 2000: -9.0; 2001: -3.8; 2002: 8.8; 2003: 8.1; 2004: 3.2; 2005: 5.7; 2006: 8.0
  - Public Debt to GDP ratio (in percent): 1999: 43.0; 2000: 45.0; 2001: 53.8; 2002: 129.7; 2003: 139.4; 2004: 127.0; 2005: 84.8; 2006: 64.0
  - Primary Fiscal Balance to GDP ratio (in percent): 1999: 0.3; 2000: 1.0; 2001: 0.5; 2002: 0.7; 2003: 2.2; 2004: 3.3; 2005: 2.6; 2006: 2.8

### V. Valuation findings on the novelty premium and market response
- Market vs theoretical prices:
  - In all scenarios explored, theoretical price is always higher than market price.
  - Novelty premium estimated by reversing the pricing model to find the discount rate that equates theoretical value to market price; gap between this implied discount rate and interest rate on traditional Argentine bonds attributed at least in part to novelty premium.
- Estimated magnitude and evolution of the novelty premium:
  - Initial premium (December 2005, first month of trading): estimated in the order of 800-1200 basis points.
  - Decline to July 2007: about 200-550 basis points (range reflects sensitivity to assumptions on GDP growth and volatility).
  - Overall decline reported: "declined rapidly by about        600 basis points during the first year and a half of trading."
  - Timing of decline: almost two thirds of the decline in the premium occurred within the first three months.
- Drivers of price increases after introduction:
  - Argentina’s strong recovery substantially raised theoretical value because payments depend on the level of GDP relative to baseline.
  - Decline in the novelty premium contributed materially to the observed price increase.
- Robustness and sensitivity:
  - Wide range of premium estimates reflects sensitivity to underlying assumptions, particularly those related to the growth and volatility of GDP.
  - Alternative scenarios and sensitivity analyses presented in Sections V and VI of the source.

### VI. Organization of the remainder of the paper (as described)
- Section II: description of introduction of GDP warrants and security details.
- Section III: market response.
- Section IV: valuation method (stochastic processes, discounting, simulation of 5,000 paths).
- Section V: baseline results (theoretical values and novelty premium estimates).
- Section VI: alternative scenarios and sensitivity analysis.
- Section VII: conclusions.

---

### Role of volatility, inflation, and exchange rate in valuation

### Role of growth volatility
- Two channels by which volatility affects value:
  - Effect on payment triggers:
    - When expected level and growth rates of GDP are sufficiently above the baseline, higher growth volatility decreases value (increasing chances of growth below threshold).
    - When expected level and growth rates are sufficiently below the baseline, higher volatility increases value (increasing likelihood of surpassing threshold).
    - When growth rates are normally distributed, this channel weakens as GDP growth rates and levels get further from baseline (operating at tails).
  - Effect on skewness of GDP:
    - If growth rates are normally distributed, GDP level is log-normal; higher variance implies higher right-skewness, increasing expected payments when level is close to trigger (call-option like).
- Interaction and dominance:
  - Channels have opposite directions for levels close to baseline.
  - In the range of exercises performed, the first channel generally dominates, so higher variance typically implies a lower value.

### Role of inflation
- One-year lag between reference period for nominal payment and actual payment produces:
  - A reduction in real value of securities in the respective currency (lag acts as an inflation tax), stronger for securities denominated in higher inflation currencies.
  - If cumulative repayments cap of 48 cents becomes binding, higher inflation can further reduce real value of payments and foreign currency value of securities denominated in higher inflation currencies.

### Role of the real exchange rate (RER)
- Excess GDP computed in constant peso terms:
  - Real appreciation of the peso increases value of constant peso payment in foreign currency terms (and vice-versa).
  - Foreign-currency-denominated warrants increase in value relative to Peso warrant in foreign currency.
- When measured in same currency, permanent change in RER has limited first-order effect except via cap on nominal payments and the one-year lag.

---

### Market response, fiscal cost, and observed prices

### Market timeline and prices
- Detachment and early quotes:
  - On November 30th 2005 the GDP-linked securities became detachable.
  - Prior suggestions for US$ warrants: about US$2 per 100 of notional value (at exchange offer).
  - Small illiquid futures market pre-detachment ranged US$3 to US$5.85.
  - At detachment US$ warrant trading at US$4.25.
  - Market analysts recommended a price about 50 percent lower than their estimated theoretical value (close to US$8).
- Subsequent evolution:
  - Market price more than doubled due to improved near-term growth outlooks and pricing corrections; sizable contribution from Argentina’s strong recovery.
  - Peak price: US$15.82 in early June 2007.
  - By mid-January 2008, trading around US$12.50.
  - Contributing factors to decline after peak: Argentina risk spread increase from about 300 basis points in June 2007 to about 450 in January 2008, and the warrant payment for December 2007.

### Fiscal implications and payments statistics
- Payments and fiscal cost:
  - In 2005 (economy growing 9.2 percent), payments associated with GDP-linked securities were US$387 million, or 0.22 percent of GDP.
  - In 2006 (growth 8.5 percent), payments in 2007 more than doubled compared to 2006, reaching US$811 millions or 0.33 percent of GDP.
  - Structural reason: payments based on level of real GDP imply higher payments as GDP recovers, imposing a higher burden on the Treasury compared to counterfactuals based on growth rates only.
- Market valuation effect:
  - Increasing market valuation of the warrant increased the ex-post market value of Argentina’s debt exchange offer substantially.

---

### Valuation methodology and baseline theoretical results

### Pricing approach and simulations
- Monte Carlo simulations:
  - For each valuation date t, draw 5,000 paths for GDP, inflation, and exchange rate up to the horizon (until 2034 in baseline exercises).
  - For each path and period compute payment per unit of currency; theoretical price at time t is average across 5,000 simulated prices.
- Theoretical value formula notation:
  - V_j(t) = sum_{k=...}^{T} E_t[C_j(k)] / (1 + r_j(k))^(k-t)  (equation (2) format described).
- Simulation frequency and inputs:
  - Theoretical values computed daily by combining slow-moving forecast data (GDP growth, inflation) with daily market data (Treasury yields, CDS risk premia, Argentine US$ discount bond yields, exchange rates).

### Discount rate construction and decomposition
- Implied yield decomposition components:
  1. Risk free rate.
  2. Default premium.
  3. Residual premium (novelty/illiquidity/data accuracy/risk-aversion/comovement effects).
- Residual premium defined as: implied yield − default premium − risk free rate.
- Discount rate construction for U.S. GDP-warrant:
  - Yield curve of zero-coupon Treasury Bill and Coupon Strips.
  - Curve for default risk implied by Argentine CDS.
  - Curve modestly shifted to match discount rate of Argentine US$ Discount bond under New York law at its duration.
  - Duration-adjusted spread of Argentine US$ Discount bond over US Treasury used to estimate default risk level.
  - Add 100 basis points (market practice) to account for data accuracy and macro forecast uncertainty (this 100 basis points does not enter calculation of residual premium).
- Peso-denominated warrant:
  - Two approaches: discount using domestic interest rate curve or convert cash flows into U.S. dollars and discount using U.S. dollar curve; authors use convert-to-dollars approach.

### Baseline GDP process and scenarios
- Main baseline GDP process:
  - Log form with persistence θ = 0.65 estimated for 1981-2006 with OLS enforcing constant mean growth rate.
  - Historical residual distribution estimated (mean μ and variance σ^2); random sampling with replacement.
  - GDP projections until 2034 derived from LACF mean growth expectations for near term, estimated persistence, and sampling residuals.
  - Two volatility values in alternative scenarios: historical Argentina standard deviation around 6 percent; emerging markets standard deviation around 4 percent.
  - Correction (-½ σ^2) added to log-process so process mean equals imposed one.
- Inflation and exchange rate processes:
  - Correlations (1991-2006, excluding pre-1991 hyperinflation period):
    - Correlation GDP and real exchange rate: -0.13
    - Correlation GDP and inflation: 0.03
    - Correlation real exchange rate and inflation: 0.24
  - Inflation variance chosen to match emerging economies’ standard deviation in last 10 years: 5.73 percent.
  - RER mean reversion coefficient set to 0.15 implying a half life of 5 years; target level is 23 percent above 2005 level.
  - Foreign inflation assumed 2.3 percent from 2006 U.S. consensus.

### Baseline theoretical values and market comparison (US$ warrant)
- Theoretical value (baseline) on December 12, 2005: US$9.99 per 100 of US$ warrant.
- Theoretical value (baseline) on July 24, 2007: US$18.61 per 100 of US$ warrant.
- Implied yields:
  - More than 20 percent at instrument detachment end-2005.
  - Around 12 percent by mid-2007.
- Residual premium (using alternative Argentine U.S. dollar-denominated bond default premium):
  - Initially almost 1200 basis points.
  - Declined by about one third within two months.
  - Remained close to around 550 basis points towards end of sample.
- Expected returns and risk metrics:
  - Expected returns on the warrant hovered around 11 percent during the sample.
  - Sharpe ratio rose from 0.22 to 0.35 (S&P 500 comparison around 0.3).

### Contributions to price increase (Dec-2005 to Jul-2007)
- Five counterfactual scenarios hold all variables but one at December 2005 levels; contribution decomposition to total price increment:
  - Expected GDP Growth Updates: 42%
  - Interaction of Macro Variables: 18%
  - Expected Exchange Rate/Inflation Updates: 5%
  - Premium Reduction (residual premium): 23%
  - Passage of Time (on the Spot Rate) / Coupon Payment: 9%
  - Discount Rate Changes: 3%
- Around 65 percent of increment due to updates in macroeconomic forecasts (42% pure GDP growth updates; 5% inflation/exchange rate; 18% interaction).

---

### Sensitivity analyses, alternative currencies, and robustness

### Comparisons with investment bank valuations
- March 2005: investment bank estimated market values for US$ warrant around US$2.15; authors' theoretical value US$6.5.
  - Many investment banks applied a 50 percent haircut on their theoretical value (their un-haircut theoretical value around US$4.3).
  - Remaining difference due largely to macroeconomic assumptions (notably long-run growth and convergence assumptions).
- End-November 2005: authors' valuation US$9.32; market reports slightly above US$8.
- Deutsche Bank theoretical value for January 2006: US$8.64.
- December 6, 2006: JP Morgan theoretical value US$17.73; authors' theoretical value US$18.22.
- Investment bank average assumptions (examples):
  - Growth converges to 3 percent by 2008-2009.
  - Growth normally distributed with standard deviation of 4 percent.
  - Inflation assumed 4 percent in the long run.
  - Equilibrium real exchange rate assumed 19 percent above 2005 level.
- Using average investment bank assumptions reduces theoretical values and residual premium; residual premium under investment bank assumptions averaged 292 basis points by July-07.

### Sensitivity to growth, volatility, and convergence
- Residual premium declines over time in all scenarios.
- Alternative scenarios compared (examples listed in source):
  - Baseline (1981-2007 residuals, 3 percent long run).
  - Investment bank assumptions (2008/09 convergence).
  - Baseline with 6% standard deviation and 3% long run.
  - Baseline with 4% standard deviation and 3% long run.
  - Baseline with LACF long run.
- Table 4 and Table 5 in source illustrate sensitivity of theoretical U.S.$ warrant values on July 24, 2007 to short-run growth shocks and to long-run convergence assumptions (exact table matrices preserved in source).

### Arg$, Euro, and robustness tests
- Arg$ warrant:
  - Theoretical value increased from Arg$8.6 (Dec-2005) to Arg$16.5 (Jul-2007).
  - Dollar warrant valued higher than peso warrant, mainly due to relatively high expected inflation in Argentina and cap on cumulative nominal payments at 48 cents of respective currency.
  - Residual premium for Arg$ securities:
    - Around 910 basis points in first two months.
    - Declined to about 650 basis points on average afterwards.
    - Legal premium hovered around 150 basis points.
    - Once legal premium accounted for, residual premiums for Arg$ and US$ securities are fairly comparable.
- Euro warrant:
  - Residual premium for Euro and US$ warrants remarkably close (robustness check).
- Exchange rate and inflation robustness:
  - Keeping RER constant at a more depreciated 2008 level reduces theoretical value of US$ warrant.
  - Lowering baseline inflation by 1 percentage point at all horizons:
    - Dollar warrant value remains unaffected (PPP assumption).
    - Peso warrant increases in value due to lower inflation during one-year lag for payment.

### Uncertainty and perfect-foresight counterfactual
- Perfect-foresight valuation (no uncertainty):
  - Theoretical values higher by more than 30 percent on average relative to baseline.
  - Implied yield under no-uncertainty scenario ~2000 basis points in December 2005 (only 75 basis points higher than baseline).
  - Under no-uncertainty scenario, implied yield declined by only 140 basis points over sample (less than baseline).
  - Interpretation: an uncertainty premium associated with risk aversion.

---

### Expected maturity, duration, and path outcomes

### Maturity probabilities and durations
- Simulation outcomes:
  - 32 percent of simulated paths for the US$ warrant reach maturity.
  - 26 percent of simulated paths for the Arg$ warrant reach maturity.
- Duration estimates by Dec-2005:
  - Arg$ warrant duration: 5.8
  - US$ warrant duration: 6.5
- Implication: a 100 basis point increment in the discount rate reduces the value of the warrant by (duration × 100 basis points).

### Forecasted cash flows and timing
- Expected cash flows (per 100 of notional) shown for 2006–2033 with discrete jumps from coupon payments (December 15 each year).
- Expected effective maturity distribution:
  - Arg$ warrant probabilities concentrate earlier than US$ warrant; Arg$ expected value peaks sooner (2008) than US$ warrant (2009).
- Figure 15 in source plots forecasted theoretical values for warrants in pesos and dollars over Jun-05 to Jun-35, ex-coupon after December 12 each year.

---

### Main conclusions, implications, and investor perceptions

### Main conclusions and valuation results
- Theoretical price computed as expected net present value of potential payments using Monte Carlo across daily/monthly/annual forecasts.
- Implied discount rate derived as rate that equates theoretical price to actual market price.
- Baseline model result: sizable reduction in premium associated with GDP-linked securities over standard Argentine bonds.
- Estimated novelty premium dynamics:
  - Premium declined on average by about 600 basis points during the first year and a half of trading.
  - Range: from 800-1200 basis points in December 2005 to 200-550 basis points in July 2007.
  - Most reduction occurred in first three months of trading.
- Sensitivities and caveats:
  - If default risk on GDP warrants is smaller than for standard bonds, the residual premium would be underestimated.
  - Theoretical price and residual premium highly sensitive to forecast assumptions, especially GDP growth.
  - Introducing possibility of sharp crises can lower theoretical valuation to observed market prices.
  - Market participants may have implicitly assigned probabilities to sharp crises not visible in available forecasts.
  - Large sensitivity to growth-process assumptions implies results should be read with extreme caution.

### Implications for future issuance and financial innovation
- If declining residual premium is due to novelty, increased familiarity from Argentina’s experience could lower novelty premia for future GDP-linked issues, encouraging other countries to contemplate issuing such instruments.
- Argentina may have provided a positive externality by incurring first-mover costs.
- Financial innovation may be associated with significant premia that decline reasonably fast.

### Appendix I — Investors’ survey (summary)
- Regulatory restrictions on holding GDP warrants (13 respondents):
  - Six indicated presence of regulatory restrictions (mainly pension funds); three negative (all from banks); four did not know.
- Required premium relative to plain-vanilla Argentine bonds:
  - Median answer: a discount rate premium between 100 and 200 basis points above standard Argentine bond valuation.
- Conditions under which investors would demand a lower rate of return (percent positive responses):
  - Government bases GDP-coupon payments on IMF-provided growth data: 57%
  - International agency announces research showing reliability of Argentine GDP data and commits to supervise data quality: 50%
  - Consultant provides free valuation software: 21%
  - Other five important emerging countries plan to issue GDP-indexed bond at the time: 21%
  - United States plans to issue GDP-indexed bond: 14%
- Main disincentives for investors (order and percentages):
  - Complexity/difficulties in valuation: 92%
  - Uncertainty about future market liquidity: 57%
  - Uncertainty about GDP data provided by government: 57%
  - Volatility of coupon payments: 29%
  - Concerns about poorer growth incentives: 7%
- Perceived default risk relative to plain-vanilla bonds:
  - "Definitely would honor": 58%
  - "Most likely would honor": 42%
  - Conclusion: warrants were not seen as riskier than conventional bonds in default terms.
- Overall interpretation:
  - Residual premium likely stems from novelty, complexity of pricing, liquidity, and data accuracy concerns; improvements in these factors plus improved economic outlook likely drove rapid price increases.

### Appendix II — Discounting cash flows (equivalence)
- Two pricing approaches for peso GDP-linked security:
  1. Discount peso cash flows using domestic interest rate curve.
  2. Convert peso cash flows into dollars and use dollar discount rate plus risk premium.
- If uncovered interest parity holds, both approaches are equivalent in expectation.
- Practical preference: authors use convert-to-dollars method due to lack of long-run Argentine nominal rate curve.

*Source: IMF Working Paper chapter titled "1.      Main Economic Indicators" (content unit: _wp08109).*

### 1.      Main Economic Indicators .......................................................................................

### 1.      Main Economic Indicators

### I. Introduction: purpose and contribution
- Purpose: quantify the cost of financial innovation by analyzing the introduction of the Argentine GDP-indexed warrants.
- Contribution: estimate a theoretically derived "novelty premium" for the Argentine GDP-warrants by comparing model-implied prices with market prices.
- Simulation approach: simulate 5,000 paths for jointly-distributed stochastic processes for GDP, inflation, and the exchange rate; compute implied warrant payments in each path.
- Key modeling elements: a discount rate and three stochastic processes (GDP, inflation, exchange rate), whose mean and volatility are based on market expectations and historical evidence.

### II. The Argentine GDP-warrants: background and issuance
- Context:
  - Argentina declared a moratorium at end-2001 and abandoned the convertibility regime in early 2002.
  - Debt in default at end-2003: US$101.2 billion (stock of debt in default).
  - Value of debt eligible for exchange lowered to US$81.8 billion.
  - Exchange concluded on June 10, 2005 with creditor participation of 76 percent.
  - Participating creditors swapped combined face-value of about US$62 billion for a new set of bonds with face-value of US$35.3 billion.
- Currency distribution of detachable GDP-linked securities (measured in Dec. 2003 Exchange Rates; in percentage of 62bn Total*):
  - Ar$ (Arg Law): 47%
  - Euro (British Law): 24%
  - US$ (NY Law): 23%
  - US$ (Arg Law): 5%
  - Yen (Japan Law): 1%
  - Source: Ministry of Economy, Rep. of Argentina
- Rationale: GDP-linked securities raised expected value of the exchange offer and acted as automatic-stabilizers by shifting payments toward favorable growth scenarios.

### III. Payment formula and contractual features
- Payment timing: payments are made on December 15 of the year following the reference year (the first payment was made in 2006). Trades are ex-dividend starting December 12.
- Payment triggers: three indicator conditions must all be met for a payment to occur:
  1. actual real GDP must exceed baseline real GDP in the reference year;
  2. growth in actual real GDP must exceed growth in baseline real GDP in the reference year;
  3. cumulative past payments should not exceed 0.48 per unit of security (in its corresponding currency).
- Payment base: if triggered, payment equals a fraction of excess GDP (difference between actual GDP and baseline GDP). The fraction equals 3.8 percent of excess GDP (76 percent participation × 5 percent).
- Formula (notation preserved from source): the coupon payment C(j)_{t+1} per unit of currency j in period t+1 (with respect to reference year t) is given by the formula in the source (see equation (1) in text), where:
  - C(j)_{t+1}: Coupon payment at time t+1 of the warrant in currency j.
  - j: Type of currency denomination: Argentine peso, U.S. dollar, Euro, or Yen.
  - Y_t: Nominal GDP in period t, in current prices.
  - y^b_t: Real GDP in baseline case (from the Debt Exchange Prospectus) for period t.
  - D_t: GDP price deflator in period t, base 1993=1.
  - ER_t: Exchange rate in Arg$ per unit of currency j in period t.
  - U(j): Unit of currency coefficient.
  - y_t: Real GDP in period t, in 1993 prices.
  - Δ: Represents the growth rate.
  - The three I(.) indicator functions equal 1 when the corresponding inequality holds, and 0 otherwise.
- Important features emphasized in the source:
  - Importance of level of real GDP: payment depends on level relative to baseline, not directly on growth rate (growth affects payment via level).
  - Discontinuity of growth effect: payments occur only when growth exceeds a threshold (about 3 percent), producing discontinuous effects around that threshold.
  - Cap on cumulative payments: cumulative payments capped at 0.48 per unit.

### IV. Key statistics and contractual quantities (as reported)
- Debt, exchange, and participation:
  - Stock of debt in default (end-2003): US$101.2 billion.
  - Value of debt eligible for exchange: US$81.8 billion.
  - Sum of notional amounts of all warrants: US$62bn (reflecting 76 percent participation).
- Table of outstanding value, unit coefficients, and first coupon as percent of original currency outstanding value (values in units of each currency; using exchange rates by Dec 31st 2003):
  - US$ (NY Law): Outstanding value 14,386 (in millions of original currency); Unit coefficient U(j) = 1/81.8; First coupon as percent of original currency outstanding value = 89.840.6245
  - US$ (Arg Law): Outstanding value 2,925; Unit coefficient = 1/81.8; First coupon percent = 18.270.6245
  - Euro (British Law): Outstanding value 11,808; Unit coefficient = (1/81.8)*(1/0.7945); First coupon percent = 78.150.6618
  - Ar$ (Arg Law): Outstanding value 86,154; Unit coefficient = (1/81.8)*(1/2.9175); First coupon percent = 559.220.6491
  - Yen (Japan Law): Outstanding value 38,369; Unit coefficient = (1/81.8)*(1/107.42292); First coupon percent = 261.200.6808
  - Total (In Dollars*): 62,318
  - Note: Unit of currency U(j) (for billions of currency j) defined as 1/81.8 multiplied by the inverse of the exchange rate in terms of currency j per dollar; sum of units times outstanding amounts equals US$62bn/US$81.8bn = 76 percent.
- Macroeconomic indicators (selected annual series 1999–2006 from Table 1; values preserved exactly):
  - Real GDP (in billions of 1993 pesos): 1999: 278.4; 2000: 276.2; 2001: 264.0; 2002: 235.2; 2003: 256.0; 2004: 279.1; 2005: 304.8; 2006: 330.6
  - GDP growth (in percent): 1999: -3.4; 2000: -0.8; 2001: -4.4; 2002: -10.9; 2003: 8.8; 2004: 9.0; 2005: 9.2; 2006: 8.5
  - CPI inflation (in percent): 1999: -1.8; 2000: -0.7; 2001: -1.5; 2002: 40.9; 2003: 3.7; 2004: 6.1; 2005: 12.3; 2006: 9.8
  - Unemployment rate (in percent): 1999: 14.5; 2000: 15.4; 2001: 16.4; 2002: 21.5; 2003: 14.5; 2004: 12.1; 2005: 10.1; 2006: 8.7
  - Current Account (In billions of US$): 1999: -12.0; 2000: -9.0; 2001: -3.8; 2002: 8.8; 2003: 8.1; 2004: 3.2; 2005: 5.7; 2006: 8.0
  - Public Debt to GDP ratio (in percent): 1999: 43.0; 2000: 45.0; 2001: 53.8; 2002: 129.7; 2003: 139.4; 2004: 127.0; 2005: 84.8; 2006: 64.0
  - Primary Fiscal Balance to GDP ratio (in percent): 1999: 0.3; 2000: 1.0; 2001: 0.5; 2002: 0.7; 2003: 2.2; 2004: 3.3; 2005: 2.6; 2006: 2.8
  - Sources: Republic of Argentina, Prospectus Supplement and Ministry of Economy and Production, and INDEC.

### V. Valuation findings on the novelty premium and market response
- Market and theoretical price relationship:
  - In all scenarios explored, the theoretical price is always higher than the market price.
  - The novelty premium is estimated by reversing the pricing model to find the discount rate that equates theoretical value to market price; the gap between this implied discount rate and the interest rate on traditional Argentine bonds is attributed at least in part to the novelty premium.
- Estimated magnitude and evolution of the novelty premium:
  - Initial premium (December 2005, first month of trading): estimated in the order of 800-1200 basis points.
  - Decline to July 2007: about 200-550 basis points (range reflects sensitivity to assumptions on GDP growth and volatility).
  - Overall decline reported: "declined rapidly by about        600 basis points during the first year and a half of trading."
  - Timing of decline: almost two thirds of the decline in the premium occurred within the first three months.
- Drivers of price increases after introduction:
  - Argentina’s strong recovery substantially raised theoretical value because payments depend on the level of GDP relative to baseline.
  - Decline in the novelty premium contributed materially to the observed price increase.
- Robustness and sensitivity:
  - Wide range of premium estimates reflects sensitivity to underlying assumptions, particularly those related to the growth and volatility of GDP.
  - The paper presents alternative scenarios and sensitivity analyses (Sections V and VI referenced for details).

### VI. Organization of the remainder of the paper (as described)
- Section II: description of introduction of GDP warrants and security details (present section).
- Section III: market response (depicted in the paper).
- Section IV: valuation method (includes stochastic processes, discounting, simulation of 5,000 paths).
- Section V: baseline results (theoretical values and novelty premium estimates).
- Section VI: alternative scenarios and sensitivity analysis.
- Section VII: conclusions.

*Source: IMF Working Paper chapter titled "1.      Main Economic Indicators" (content unit: _wp08109).*

### 2.9 percent will imply none. This discontinuity is perceived by investors to contribute

### _wp08109 - 2.9 percent will imply none. This discontinuity is perceived by investors to contribute

### Role of growth volatility
- Volatility affects the value of the GDP-linked security through two channels:
  - Effect of volatility on payment triggers:
    - When expected level and growth rates of GDP are sufficiently above the baseline, higher growth volatility decreases the value of the GDP-linked security (increasing chances of a growth rate below the threshold for payment).
    - When expected level and growth rates are sufficiently below the baseline, higher volatility increases the value of the security (increasing likelihood of surpassing the threshold).
    - When growth rates are normally distributed, this channel weakens as GDP growth rates and levels get further from their baseline (operating at distribution tails where density is small).
    - The channel implicitly includes two effects: one on the level and one on growth rates.
  - Effect of volatility on skewness of GDP:
    - If growth rates are normally distributed, the level of GDP is log-normal; higher variance implies higher right-skewness (thicker density towards the right tail).
    - Higher right skewness implies that, when the level of GDP is close to the trigger level, payments can be expected to be higher on average (similar to a standard call option).
- Interaction and dominance:
  - The two channels have opposite directions for levels close to the baseline imposed by the contract.
  - Both channels are more powerful the closer the path is to the baseline (higher variance implies more zero-cash flows from the first channel, but more right skewness from the second).
  - For paths sufficiently far from the trigger rate and level, the second effect tends to dominate.
  - In the range of exercises performed, the first channel generally dominates, so higher variance typically implies a lower value.

### Role of inflation
- Payment determination features a one-year lag between the reference period for nominal payment and the time it is actually paid, producing two effects:
  - The lag reduces the real value of the securities in the respective currency; the reduction is stronger for securities denominated in higher inflation currencies (the lag acts as an inflation tax). When compared in the same currency, securities denominated in higher inflation currencies would lose value relative to others, as long as higher inflation currencies do not appreciate.
  - If the sum of total repayments is capped at 48 cents of the respective currency, higher inflation can further reduce the real value of payments if that cap becomes binding (and reduce the foreign currency value of securities denominated in higher inflation currencies relative to securities denominated in lower inflation currencies).

### Role of the real exchange rate (RER)
- Excess GDP is computed in constant peso terms.
  - A real appreciation of the peso increases the value of the constant peso payment in foreign currency terms (and vice-versa for depreciation).
  - Consequently, foreign-currency-denominated warrants increase in value relative to the Peso warrant in the foreign currency.
- When measured in the same currency, as a first approximation, payments and values of warrants denominated in different currencies would be unaffected by a permanent change in the real exchange rate, except for:
  - The cap on nominal payments.
  - The one-year lag between determination and actual payment (similar to inflation effects above).

### Market response (Argentina GDP warrants)
- Timeline and market prices:
  - On November 30th 2005—180 days after the settlement of the debt exchange—the GDP-linked securities became detachable, creating a market for the warrants.
  - At the time of the exchange offer, major investment banks suggested a price for the US$ warrants of about US$2 per 100 of notional value.
  - In the months before detachment (after June 10th), a small illiquid futures market had prices ranging from US$3 to US$5.85.
  - At detachment, the US$ warrant was trading at US$4.25.
  - Market analysts recommended a price about 50 percent lower than their estimated theoretical value (close to US$8), citing novelty and other issues.
- Subsequent market evolution:
  - Market price more than doubled due to improved near-term growth outlooks and pricing corrections; a sizable contribution came from Argentina’s strong recovery (theoretical value highly sensitive to early-year growth).
  - Asset managers recommended long positions until June 2007, when news about an energy crisis reduced growth forecasts.
  - Peak price: US$15.82 in early June 2007.
  - By mid-January 2008, trading around US$12.50.
  - Contributing factors to decline: Argentina risk spread increase from about 300 basis points in June 2007 to about 450 in January 2008, and the warrant payment for December 2007.

### Fiscal implications and payments statistics
- Payments and fiscal cost:
  - In 2005, with the economy growing 9.2 percent, payments associated with the different GDP-linked securities were US$387 million, or 0.22 percent of GDP.
  - In 2006, growth was 8.5 percent, yet payments in 2007 more than doubled compared to 2006, reaching US$811 millions or 0.33 percent of GDP.
  - Structural reason: payments based on the level of real GDP (rather than growth rate) imply higher payments as GDP recovers, imposing a higher burden on the Treasury compared to a counterfactual where payments depended exclusively on reference-year growth.
- Market valuation effect:
  - Increasing market valuation of the warrant increased the ex-post market value of Argentina’s debt exchange offer substantially.

### Theoretical value and valuation methodology
- Pricing approach:
  - Use of Monte Carlo simulations is the common market method; price equals discounted value of all expected coupon payments (instrument pays coupons only, no principal).
  - The theoretical value of currency j warrant:
    - V_j(t) = sum_{k=...}^{T} E_t[C_j(k)] / (1 + r_j(k))^(k-t)  (equation (2) format described in text).
  - 5,000 paths for GDP, inflation, and exchange rate are drawn for each time t; theoretical price at time t is the average of the 5,000 resulting prices.
- Discount rate considerations:
  - Argument points:
    - Instrument only pays during good growth years; thus should carry less default risk than standard bonds, but persistently poor growth would dampen this advantage.
    - Moral hazard and investor concerns about data accuracy can raise the premium (market surveys noted data accuracy concerns).
    - Risk aversion could increase premium since returns are more volatile.
    - Correlation with market portfolio matters; Argentina’s GDP growth shows very little correlation with international stock market indices (implying diversifiable idiosyncratic risk for international investors), but high correlation with domestic indices implies local investors should use a higher discount rate (positive beta).
  - Market practice and construction:
    - Financial markets used discount rates at least as high as Argentine plain-vanilla US$ bonds.
    - Construct the discount rate for the U.S. GDP-warrant by adding:
      - Yield curve of zero-coupon Treasury Bill and Coupon Strips,
      - Curve for default risk implied by the Argentine Credit Default Swap (CDS),
      - Curve modestly shifted to match discount rate of the Argentine US$ Discount bond under New York law at its duration.
    - Estimate of default risk level uses duration-adjusted spread of the Argentine US$ Discount bond over the US Treasury bond matching that duration.
    - Add 100 basis points (common investment bank practice) to account for market concerns about data accuracy and macro forecast uncertainty. Note: this additional spread of 100 basis points will not enter the calculation of the residual premium paid by the warrants.
  - For peso-denominated warrant:
    - Two possibilities: discount using domestic interest rate curve (requires additional assumptions) or convert cash flows into U.S. dollars and discount using the U.S. dollar curve above.
    - Under uncovered interest parity, the two approaches should deliver the same result; the second method (convert to U.S. dollars then discount) is used.
- GDP process and scenarios:
  - GDP process specified in log form with persistence and residual error (equation (3) in text).
  - Main baseline:
    - Equation estimated for 1981-2006 using OLS imposing a constant mean growth rate.
    - Estimated persistence θ = 0.65.
    - Historical distribution of residuals estimated (mean μ and variance σ^2).
    - GDP projections until 2034 derived from: mean growth expectations from Latin America Consensus Forecast (LACF); estimated persistence; random sampling with replacement from estimated residual distribution.
    - 5,000 different GDP paths generated, producing a shock distribution resembling Argentina’s past with occasionally large negative shocks.
  - Alternative GDP processes:
    - Error terms modeled as geometric Brownian motion with given variance (scenarios where large crises are unlikely).
    - Two volatility values used:
      - Historical standard deviation for Argentina: around 6 percent.
      - Emerging markets standard deviation: around 4 percent.
  - Forecast inputs and frequency:
    - Mean growth expectations for next two years from LACF monthly issues.
    - Forecasts for years 3 to 10 from biannual LACF issues.
    - Remaining years until 2034 use Argentine authorities’ original long-run projection of 3 percent.
    - Non-monthly forecasts interpolated linearly to monthly frequency.
    - Volatility in the first projection year reduced linearly from January to December to reflect lower early-year uncertainty.
  - Note: a correction (-½ σ^2) is added to the log-process to ensure the process mean equals the imposed one.

### Inflation and exchange rate processes
- Jointly distributed shocks for macro variables with correlations (1991-2006):
  - Correlation GDP and real exchange rate: -0.13
  - Correlation GDP and inflation: 0.03
  - Correlation real exchange rate and inflation: 0.24
  - Correlations computed excluding pre-1991 hyperinflation period.
- Inflation processes:
  - Two inflation series: GDP deflator inflation (D_t) and CPI inflation.
  - Shocks modeled with chi-square distribution, mean set to expected value.
  - Mean CPI inflation forecasts from LACF (monthly for 2-year horizons, biannual for 3-10 years, constant thereafter), interpolated to monthly.
  - GDP deflator inflation uses IMF World Economic Outlook (WEO) information.
  - Variance for inflation processes chosen to match emerging economies’ standard deviation in last 10 years: 5.73 percent.
- Real exchange rate (RER) and nominal exchange rate:
  - RER projections for first two years based on forward nominal exchange rates and CPI inflation forecasts (foreign inflation assumed 2.3 percent from 2006 U.S. consensus).
  - For remaining horizon, RER follows a mean-reverting process towards the 50-year average real exchange rate; the target level is 23 percent above the 2005 level.
  - Standard deviation calibrated to match RER standard deviation in 1991-2006 (BCRA data).
  - Mean reversion coefficient set to 0.15 implying a half life of 5 years (Rogoff, 1996).
  - Nominal exchange rate projections use forward for first two years; thereafter derived from RER and CPI processes.
- Simulation details:
  - For each time t, simulate 5,000 paths for time series of these variables up to the horizon.

*Source: Excerpt from IMF working paper content unit provided.*

### 2034. For each path, we calculate the payment per unit of currency in each period, and the

### _wp08109 - 2034. For each path, we calculate the payment per unit of currency in each period, and the

### Methodology and Valuation Procedure
- Theoretical values computed by averaging 5,000 simulated path values for each time t.
- Theoretical values were computed daily by combining: slow-moving forecast data (GDP growth, and inflation) with daily market data (Treasury yields, CDS risk premia, Argentine US$ discount bond yields, and exchange rates).
- Implied yield for a given market price is decomposed into three components: (1) the risk free rate, (2) a default premium, (3) a residual premium (novelty/illiquidity/data accuracy/risk-aversion/comovement effects).
- Residual premium = implied yield − default premium − risk free rate (proxy uses U.S. treasury bond of similar duration; duration goes from 7 years at detachment to around 6 years in July 2007).
- Implicit default premium obtained by shifting the CDS default risk curve to match yield differences between Discount bond and U.S. Treasury Bill for same duration.

### Baseline Theoretical Values and Market Prices (US$ warrant)
- Theoretical value (baseline) on December 12, 2005: US$9.99 per 100 of US$ warrant.
- Theoretical value (baseline) on July 24, 2007: US$18.61 per 100 of US$ warrant.
- Market prices available from Bloomberg from December 2005 onwards; theoretical vs market evolution shown in Figure 4 (document).

### Implied Yields, Residual Premiums, and Expected Returns
- Implied yields:
  - More than 20 percent at instrument detachment end-2005.
  - Around 12 percent by mid-2007.
- Residual premium (if default premium from alternative Argentine U.S. dollar-denominated bonds applied to warrant):
  - Initially almost 1200 basis points.
  - Declined by about one third within two months.
  - Remained close to around 550 basis points towards end of sample.
- Expected returns on the warrant hovered around 11 percent during the sample.
- Volatility of returns decreased over the interval; Sharpe ratio rose from 0.22 to 0.35 (S&P 500 comparison around 0.3).
- Residual premium provides an upper bound on novelty premium; should decline as market develops.

### Factors Explaining Price Changes (Dec-2005 to Jul-2007)
- Five counterfactual scenarios constructed (holding all variables but one at December 2005 levels; a fifth holds all constant to gauge passage of time):
  - Variables varied individually: (i) GDP, (ii) inflation/exchange rate (allowed to move together), (iii) discount rate (U.S. interest rate plus proxy for default risk), (iv) residual premium; fifth: passage of time.
- Contributions to price increase between December 2005 and July 2007 (percentage of total increment):
  - Expected GDP Growth Updates: 42%
  - Interaction of Macro Variables: 18%
  - Expected Exchange Rate/Inflation Updates: 5%
  - Premium Reduction (residual premium): 23%
  - Passage of Time (on the Spot Rate) / Coupon Payment: 9%
  - Discount Rate Changes: 3%
- Around 65 percent of increment due to updates in macroeconomic forecasts for whole horizon (42% pure GDP growth realizations and forecast updates; 5% inflation/exchange rate; 18% interaction).

### Comparisons with Investment Bank Valuations
- March 2005: investment bank estimated market values for US$ warrant around US$2.15; authors' theoretical value US$6.5.
  - Many investment banks applied a 50 percent haircut on their theoretical value (their un-haircut theoretical value around US$4.3).
  - Remaining difference due largely to macroeconomic assumptions (notably long-run growth and convergence assumptions).
- End-November 2005: authors' valuation US$9.32; market reports slightly above US$8.
- Deutsche Bank theoretical value for January 2006: US$8.64.
- Early March 2006: major investment banks updated valuations (new growth forecasts and lower discount rates), causing a 27 percent single-week price increase.
- December 6, 2006: JP Morgan theoretical value US$17.73; authors' theoretical value US$18.22.
- Investment banks tended to assume:
  - Growth converges to 3 percent by 2008-2009.
  - Growth normally distributed with standard deviation of 4 percent.
  - Inflation assumed to be 4 percent in the long run.
  - Equilibrium real exchange rate assumed 19 percent above 2005 level.
- Using average investment bank assumptions reduces theoretical values and residual premium; residual premium under investment bank assumptions averaged 292 basis points by July-07.

### Sensitivity Analyses: Growth, Volatility, and Convergence
- Residual premium across scenarios declines over time in all scenarios.
- Alternative scenarios compared in Figure 9:
  - Baseline (1981-2007 residuals, 3 percent long run).
  - Investment bank assumptions (2008/09 convergence).
  - Baseline with 6% standard deviation and 3% long run.
  - Baseline with 4% standard deviation and 3% long run.
  - Baseline with LACF long run.
- Table 4 (theoretical U.S.$ warrant values on July 24, 2007) — sensitivity to 2007/2008 growth +/- 1.5%:
  - For combinations of 2007 Growth (rows) and 2008 Growth (columns):
    - 2007=7.00, 2008=5.5 (Baseline)  => 9.00; 2008=4.00 => 19.40; 2008=7.00 => 18.70; 2008=?
    - 2007=7.5 (Baseline) and 2008 values => 18.62, 17.93, 17.21 (table presents matrix form; source: authors' estimates).
  - (Table presented in source; baseline by July 24th, 2007, based on Consensus Forecast Expectations.)
- Table 5 (sensitivity on convergence year; long run expected growth examples):
  - Long Run Expected Growth 2.50 => Theoretical Values: 14.60, 17.07, 17.75 for years 2009/2014/2018 (Baseline indicated).
  - Long Run 3.00 (Baseline) => 15.87, 17.52, 17.93.
  - Long Run 3.50 => 17.10, 17.96, 18.11.
  - Faster convergence lowers theoretical valuation; long-term growth of 2.5 percent (below payment threshold) can still yield positive payments due to variance of GDP process.

### Other Valuation Exercises: Arg$, Euro, and Robustness Tests
- Arg$ warrant (valuation method converts expected cash flows to dollar terms using exchange rate at payment; discount with dollar discount rate; transform back to pesos using valuation-day exchange rate):
  - Theoretical value increased from Arg$8.6 (Dec-2005) to Arg$16.5 (Jul-2007).
  - Per-unit notional: dollar warrant valued higher than peso warrant, mainly due to relatively high expected inflation in Argentina and cap on cumulative nominal payments at 48 cents of respective currency.
  - Legal premium for Arg$ warrant estimated by comparing yields of dollar warrants under New York Law vs Argentine Law; spread is an upper bound on legal premium (liquidity and domestic investor composition may also influence spread).
  - Residual premium for Arg$ securities:
    - Around 910 basis points in first two months.
    - Declined to about 650 basis points on average afterwards.
    - Legal premium hovered around 150 basis points.
    - Once legal premium accounted for, residual premiums for Arg$ and US$ securities are fairly comparable.
- Euro warrant:
  - Theoretical pricing using same method; residual premium for Euro and US$ warrants remarkably close (robustness check).
- Exchange rate and inflation robustness:
  - Keeping real exchange rate constant at projected 2008 level (more depreciated real exchange rate) reduces theoretical value of US$ warrant.
  - Lowering baseline inflation by 1 percentage point at all horizons:
    - Dollar warrant value remains unaffected (PPP assumption).
    - Peso warrant increases in value due to lower inflation during one-year lag for payment.

### Effect of Uncertainty and Perfect-Foresight Counterfactual
- Perfect-foresight (forecasted GDP, exchange rates, inflation realized with probability one) valuation results:
  - Theoretical values higher by more than 30 percent on average relative to baseline.
  - Implied yield under no-uncertainty scenario ~2000 basis points in December 2005 (only 75 basis points higher than baseline).
  - Under no-uncertainty scenario, implied yield declined by only 140 basis points over sample (less than baseline).
  - The higher yield under no-uncertainty view interpreted as an uncertainty premium; investors’ risk aversion affects magnitude of this premium.

### Expected Value for Remaining Maturity and Path Outcomes
- Forecast of theoretical price from 2007 until maturity based on July 2007 macro forecasts; future discount factors from yield curve using expectations hypothesis.
- In theory, positive measure of payments in all periods (some projections produce payments), but in reality warrants may stop paying once 48 percent cap reached and third condition fails.
- Argentina’s inflation projections imply peso warrant likely to expire sooner than US$ warrant (cap reached sooner).
- Payments in respective currency can be expected higher for Arg$ warrant than US$ warrant (nominal exchange rate expected to neutralize most inflation differential).
- Simulation outcomes:
  - 32 percent of simulated paths for the US$ warrant reach maturity.
  - 26 percent of simulated paths for the Arg$ warrant reach maturity.
- Duration estimates by Dec-2005:
  - Arg$ warrant duration: 5.8
  - US$ warrant duration: 6.5
  - By definition, a 100 basis point increment in the discount rate reduces the value of the warrant by (duration × 100 basis points) — (document provides duration definitions and implications).

*Source: Bloomberg and authors' estimates.*

### 5.8 and 6.5 percent approximately.

### _wp08109 - 5.8 and 6.5 percent approximately.

### Forecasts, Expected Cash Flows, and Theoretical Warrant Values
- 5.8 and 6.5 percent approximately.
- Expected cash flows (per 100 of notional value) for the US$ and AR$ warrant are shown over the period 2006–2033, with discrete jumps arising from coupon payments (coupons due on December 15 of each year, starting 2006) and progressive increases within intervals due only to the passage of time on the spot rate.
- The expected effective maturity distribution for the US$ and AR$ warrant shows differing timing: probabilities for the Ars$ warrant concentrate earlier than for the US$ warrant; for example, by 2030 the cumulative probabilities cited show the Ars$ warrant probabilities dominating earlier years relative to the US$ warrant.
- The shorter duration of the Ars$ warrant is reflected in its expected value peaking sooner—in the forecast period—than the expected value of the US$ warrant (2008 versus 2009).
- Figure 15: Forecasted theoretical values for the warrants in pesos and dollars are plotted as units of currency per 100 of notional value over the horizon Jun-05 to Jun-35. Values are ex-coupon after December 12 of each year; coupon payments on December 15 produce discrete jumps.

### Main Conclusions and Valuation Results
- The theoretical price for the Argentine GDP warrant was calculated as the expected net present value of potential payments using a Monte Carlo exercise applied to daily, monthly, and annual forecasts for the determinants of the payments.
- The implied discount rate is derived as the rate that makes the theoretical price match the actual price.
- Baseline model result: a sizable reduction in the premium associated with GDP-linked securities over the standard Argentine bonds.
- Estimated novelty premium dynamics:
  - Premium declined on average by about 600 basis points during the first year and a half of trading.
  - Range of premium: from a range of 800-1200 basis points in December 2005 to a range of 200-550 in July 2007.
  - Most of the reduction took place in the first three months of trading.
- Sensitivities and caveats:
  - If default risk on GDP warrants is smaller than for standard bonds, the residual premium of GDP-linked securities over standard Argentine bonds would be underestimated.
  - Theoretical price and residual premium are highly sensitive to forecast assumptions, especially for GDP growth.
  - Introducing the possibility of sharp crises in the baseline growth process can lower theoretical valuation to observed market prices.
  - Market participants may have implicitly assigned a probability to sharp crises not visible in available forecasts (which mainly report only the first moment of expectations).
  - Large sensitivity to growth-process assumptions implies results should be read with extreme caution.
- Implications for future issuance:
  - If declining residual premium is due to novelty, increased familiarity from the Argentine experience could lower novelty premia for future GDP-linked issues, encouraging other countries to contemplate issuing such instruments.
  - Argentina may have provided a positive externality by incurring first-mover costs.
  - Financial innovation may be associated with significant premia that decline reasonably fast.

### Appendix I — Investors’ Survey (Summary and Implications)
- Survey context: Fernandez et al. (2006) survey (investors participating in the debt exchange) implemented in mid 2005 prior to detachment of GDP warrants from plain-vanilla bonds; based on Borensztein et al. (2004).
- Regulatory restrictions on holding GDP warrants:
  - Thirteen respondents: six indicated presence of regulatory restrictions (mainly pension funds), three negative (all from banks), four did not know.
- Required premium relative to plain-vanilla Argentine bonds:
  - Median answer: a discount rate premium between 100 and 200 basis points above the one used for valuation of a standard Argentine bond.
  - This is notable because theory suggests GDP-indexed bonds should be subject to a smaller default risk than regular bonds.
- Conditions under which investors would demand a lower rate of return (non-mutually exclusive; percentage of positive responses):
  - Argentina’s government accepts to base GDP-coupon payments on growth data provided by the IMF (57%).
  - An international agency announces that their research shows the reliability of Argentine GDP data and commits to supervise the quality of future data (50%).
  - A consultant agency announces that it’s going to provide a free software with a formula to value the growth coupon (21%).
  - Other five important emerging countries plan to issue a GDP-indexed bond at the time (21%).
  - The United States plans to issue a GDP-indexed bond (14%).
- Main disincentives for investors holding the instrument (non-mutually exclusive; order of importance with percentages where provided):
  - Complexity of the instrument and/or difficulties in the valuation (92%).
  - Uncertainty about market liquidity in the future (57%).
  - Uncertainty about GDP data provided by the government (57%).
  - Volatility of coupon payments (29%).
  - Concerns about poorer growth incentives (7%).
- Perceived default risk relative to plain-vanilla bonds:
  - Responses: "definitely would honor" (58%) and "most likely would honor" (42%) — only these two categories were chosen.
  - Conclusion: GDP warrants were not seen as riskier than conventional bonds in terms of default risk; premium differential is unlikely to reflect default risk.
- Overall interpretation:
  - Residual premium likely stems from novelty, complexity of pricing, liquidity, and data accuracy concerns.
  - Improvements in perception of these factors, coupled with improved economic outlook, likely drove the rapid increase in price observed in the last year.

### Appendix II — Discounting Cash Flows (Equivalence of Approaches)
- Two possibilities for pricing the peso GDP-linked security:
  1. Discount peso cash flows using the domestic interest rate curve.
  2. Convert peso cash flows into dollars and use the dollar discount rate plus a risk premium.
- Notation:
  - R(t) and R*(t): real interest rate in Argentina and the U.S., respectively.
  - r(t) and r*(t): respective nominal interest rates.
  - C(Arg$)k: defined in the text as the k-th cash flow in Arg$.
- First method price in pesos in period t (formula structure shown in text): sum over k from 1 to T of discounted Arg$ cash flows using an Arg$ nominal rate structure.
- Second method price uses the local currency nominal rate and exchange rate expectations (formula structure shown in text).
- If uncovered interest parity holds:
  - E_t(ER_{t+1})/ER_t + r_t = r_t^* + ... (as given in text), and in expectations both formulas are equivalent.
- Practical note:
  - Lack of a curve for the nominal rate in Argentina for the long run leads authors to prefer the second method (convert to dollars and use dollar discount rate plus risk premium).

*Source: Authors' estimates and survey results as presented in the IMF working paper excerpt.*

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