## 1. VIX and VDAX Indices

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### Introduction and scope
- Volatility in mature equity markets rose since late 2006 with a spike in mid-2007 (subprime crisis) and remained elevated into 2008, though below peaks in 1998 and 2001–03.
- Paper examines forex returns for five East Asian countries: Indonesia (IDN), Korea (KOR), Philippines (PHL), Singapore (SGP), and Thailand (THA).
- Full sample period: 2001–07.
- Central hypothesis: volatility shifts in mature markets transmit to emerging market foreign exchange returns via portfolio reallocations (search-for-returns and flight-to-safety), with implications for monetary and exchange rate management.

### Methodology and data
- Modeling framework: AR-GARCH specification for forex returns and conditional variance (Engel (1982); Bollerslev (1986)).
- Return equation (as specified):
  - dlx_t = φ_0 + ∑_{i=1}^m φ_i dlx_{t-1} + ∑_{i=1}^n θ_i z_{it} + ∑_{i=1}^k π_i Ω_{it} + ε_t
  - ε_t = σ_t^{1/2} η_t, η_t ~ i.i.d. (0, 1).
- Conditional variance specification:
  - σ_t^2 = α_0 + α_1 ε_{t-1}^2 + β_1 σ_{t-1}^2
- Long-run elasticity of forex returns to mature market volatility: ∑_{i=1}^k π_i / (1 – ∑_{i=1}^m φ_i).
- Conditions for well-defined variance: α_0, α_1, β_1 ≥ 0 and α_1 + β_1 < 1; finite unconditional variance = α_0/(1–α_1–β_1).
- Mature market volatility proxies:
  - VIX (CBOE volatility index, forward-looking for S&P500).
  - VDAX (implied volatility of the DAX, 30-day DAX option contracts).
- Euro and yen forex returns included as regressors to proxy global developments.
- Interest rate differentials not explicitly included (assumed proxied by lagged forex returns).

### Pre-estimation diagnostics
- Log exchange rate series (lx_t) were I(1); first differences I(0). VIX index I(1).
- AIC suggested two lags of dependent variable and regressors in estimation equations.
- Granger causality tests did not reject the null that VIX does not Granger cause East Asian exchange rates.
- Squared returns showed persistence/clustering; ARCH tests supported GARCH formulation.
- Error distributions were skewed and leptokurtic → generalized exponential distribution (GED) used for errors (GED parameter fixed at 1.5).

### GARCH estimation specifications
- Baseline models: AR(2)-GARCH(1,1) with VIX (and separately VDAX) as regressors.
- Error distribution: generalized error distribution (GED), GED parameter fixed at 1.5.
- Included observations (VIX models): 1822 after adjustments.
- Significance: coefficients on VIX highly significant in all VIX-based models; conditional variance coefficients (α_1, β_1) significant and nonnegative with α_1 + β_1 < 1.

### Empirical results — sensitivity of forex returns to mature equity market volatility
- Main finding: increase in mature market equity volatility associated with lower forex returns (exchange rate depreciation) for all five East Asian economies — evidence of a “flight-to-safety” effect.
- Reported range of long-run elasticities of East Asian forex returns to mature equity market volatility: 0.03 to 0.1.
  - Interpretation: a 5 percentage point increase in the VIX index was associated, on average, with 0.15–0.4 percentage point exchange rate depreciation.
- Cross-country ordering of sensitivity: IDN at the higher end; KOR and SGP middle; PHL and THA lower.
- VIX_GARCH model coefficient summary (Sample period: 2001-07):
  - VIX: IDN -0.08; KOR -0.06; PHL -0.03; SGP -0.04; THA -0.03
  - Euro/$: IDN 0.07; KOR 0.14; PHL 0.02; SGP 0.08; THA 0.07
  - Yen/$: IDN 0.04; KOR 0.13; PHL 0.03; SGP 0.00; THA 0.00

### Volatility: conditional and unconditional measures
- Unconditional variances and standard deviations from VIX_GARCH models (Sample period: 2001-07):
  - Unconditional Variance: IDN 1.00; KOR 0.14; PHL 0.12; SGP 0.07; THA 0.09
  - Unconditional SD: IDN 1.00; KOR 0.37; PHL 0.34; SGP 0.27; THA 0.30
- Patterns:
  - KOR, SGP, and THA: conditional volatilities converge toward unconditional volatilities with episodes of “excess” volatility followed by moderation.
  - PHL and IDN (especially IDN): elevated conditional volatility early in the sample biased unconditional volatility upward.

### Subsample analysis and stylized facts
- Subsamples defined:
  - 2001–2003Q2 (generally elevated VIX/VDAX).
  - 2003Q3–07 (more moderate VIX/VDAX).
- VIX_GARCH subsample results (selected figures):
  - Sample period: 2001-03Q2 — VIX elasticities: IDN -0.04; KOR -0.03; PHL 0.00; SGP -0.03; THA -0.03
    - Unconditional Variance: KOR 0.21; PHL 0.23; SGP 0.08; THA 0.07
    - Unconditional SD: KOR 0.45; PHL 0.48; SGP 0.28; THA 0.27
  - Sample period: 2003Q3-07 — VIX elasticities: IDN -0.09; KOR -0.08; PHL -0.05; SGP -0.05; THA -0.02
    - Unconditional Variance: IDN 0.25; KOR 0.11; PHL 0.13; SGP 0.06; THA 0.24
    - Unconditional SD: IDN 0.50; KOR 0.33; PHL 0.36; SGP 0.25; THA 0.49
- Stylized interpretations:
  - General result holds: higher mature market volatility → depreciation of East Asian currencies.
  - Elasticities generally higher during 2003Q3–07, possibly reflecting greater integration of East Asian asset markets into the global economy.
  - Elasticities remained negative during 2006–07 and increased in magnitude for some countries (especially the Philippines), indicating exposure to subprime-related “fears.”
  - Long-run exchange rate volatility tended to be higher in the earlier subsample; long-run volatility appears to have fallen as fundamentals strengthened and markets acclimatized to new regimes.
- Country-specific notes:
  - IDN experienced the highest forex volatility among sample countries.
  - SGP measured the lowest volatility, partly due to tighter exchange rate management.
  - KOR and SGP exhibited steady conditional and unconditional volatility.
  - PHL: unconditional volatility fell in the latter subsample, but conditional volatility rose.
  - THA: increase in unconditional and conditional volatility, partly related to political uncertainties in 2006.

### Robustness checks
- VDAX substituted for VIX (correlation between VIX and VDAX: 0.88). VDAX was more volatile than VIX over the sample.
- VDAX-based GARCH estimates: broadly similar results; long-run elasticities to VDAX generally a bit smaller than to VIX; unconditional variances and standard deviations differences negligible.
- VDAX_GARCH models (Sample period: 2001–07) — reported figures:
  - VDAX elasticities: IDN -0.06; KOR -0.07; PHL -0.02; SGP -0.02; THA -0.02
  - Unconditional Variance: IDN 0.97; KOR 0.14; PHL 0.13; SGP 0.07; THA 0.10
  - Unconditional SD: IDN 0.99; KOR 0.37; PHL 0.36; SGP 0.27; THA 0.31
- Additional robustness: alternative lag lengths (one lag for KOR, PHL, SGP, THA; three for IDN) produced nearly the same parameter estimates for VDAX elasticities and unconditional moments.
- VDAX subsample results (selected):
  - Sample period: 2001-03Q2 — VDAX elasticities: IDN -0.02; KOR -0.05; PHL -0.00; SGP -0.02; THA -0.02
    - Unconditional Variance: IDN 7.98; KOR 0.20; PHL 0.28; SGP 0.08; THA 0.07
    - Unconditional SD: IDN 2.82; KOR 0.45; PHL 0.53; SGP 0.28; THA 0.27
  - Sample period: 2003Q3-07 — VDAX elasticities: IDN -0.09; KOR -0.08; PHL -0.04; SGP -0.04; THA -0.02
    - Unconditional Variance: IDN 0.25; KOR 0.11; PHL 0.13; SGP 0.07; THA 0.31
    - Unconditional SD: IDN 0.50; KOR 0.33; PHL 0.36; SGP 0.26; THA 0.56

### Conclusions — key takeaways
- During 2001–07, forex returns for Indonesia, Korea, Philippines, Singapore, and Thailand declined when mature market equity volatility rose — consistent with a “flight-to-safety” effect.
- GARCH estimates suggest that a 5 percentage point increase in mature market equity volatility was associated with an exchange rate depreciation of up to ½ percent.
- Sensitivity of East Asian exchange rates to mature market volatility rose during the later sample period, suggesting greater global integration.
- Estimated GARCH models provide unconditional standard deviations as operational measures of “long-term” and “excess” volatility; a key finding is that long-run forex volatility declined over the sample, possibly reflecting stronger fundamentals and adaptation to more flexible regimes alongside lower mature market volatility.

*Source: _wp08208 - References (PDF chapter/section, sample content pages 3–31).*

### 1. VIX and VDAX Indices.................................................................................................

### 1. VIX and VDAX Indices

### Major sections listed
- 1. VIX and VDAX Indices ..................................................................................................11
- 2. Exchange Rates ...............................................................................................................12
- 3. Daily Forex Returns ........................................................................................................13
- 4. Daily Squared Forex Returns..........................................................................................14
- 5. FIX_AR(2)-GARCH(1,1) Models: Residuals ................................................................15
- 6. VIX AR(2)-GARCH(1,1) Models: Squared Residuals ..................................................16
- 7. Daily Conditional and Unconditional Volatilities: 2001–07 ..........................................17
- 8. Daily Conditional and Unconditional Volatilities: VIX Models, 2001-03Q2 ................18
- 9. Daily Conditional and Unconditional Volatilities: VIX Models, 2003Q3–07 ...............19
- 10. Daily Conditional and Unconditional Volatilities: VIX Models, 2001–07 ....................20

### Analytical components implied by section headings
- Indices coverage:
  - VIX and VDAX indices analysis (section 1).
- Exchange rate data:
  - Exchange Rates (section 2).
  - Daily Forex Returns (section 3).
  - Daily Squared Forex Returns (section 4).
- Time series and volatility modeling:
  - FIX_AR(2)-GARCH(1,1) model residuals (section 5).
  - VIX AR(2)-GARCH(1,1) model squared residuals (section 6).
  - Daily conditional and unconditional volatilities across multiple samples (sections 7–10), with subdivisions:
    - 2001–07 (section 7 and 10).
    - VIX models split into 2001-03Q2 (section 8) and 2003Q3–07 (section 9).

### Key temporal and model specifications (verbatim)
- Time spans and sample splits:
  - 2001–07
  - 2001-03Q2
  - 2003Q3–07
- Model specifications referenced:
  - FIX_AR(2)-GARCH(1,1)
  - VIX AR(2)-GARCH(1,1)

### Tables (listed)
- 1. Daily Foreign Exchange Return: Summary Statistics ....................................................21
- 2. VIX and VDAX Indices: Summary Statistics ................................................................22
- 3. Exchange Rates and Volatility Indices: Augmented Dickey-Fuller Test Statistics........23
- 4. VAR Lag Order Selection Criteria .................................................................................24
- 5. Forex Returns and VIX AR(2)-GARCH(1,1) Models, 2001–07....................................25
- 6. Forex Returns and VIX AR(2)-GARCH(1,1) Models, 2001–03Q2...............................26
- 7. Forex Returns and VIX AR(2)-GARCH(1,1) Models, 2003Q3–07...............................27
- 8. Forex Returns and VDAX AR(2)-GARCH(1,1) Models, 2001–07 ...............................28
- 9. Forex Returns and VDAX AR(2)-GARCH(1,1) Models, 2001–03Q2 ..........................29
- 10. Forex Returns and VDAX AR(2)-GARCH(1,1) Models, 2003Q3–0 ............................30

*Source: _wp08208 - 1. VIX and VDAX Indices.................................................................................................*

### References..............................................................................................................

### _wp08208 - References

### Introduction: context and scope
- Volatility in mature equity markets rose since late 2006 with a spike in mid-2007 (subprime crisis) and remained elevated into 2008, though below peaks in 1998 and 2001–03.
- The paper examines forex returns for five East Asian countries: Indonesia (IDN), Korea (KOR), Philippines (PHL), Singapore (SGP), and Thailand (THA).
- Full sample period: 2001–07.
- Central hypothesis: volatility shifts in mature markets transmit to emerging market foreign exchange returns via portfolio reallocations (search-for-returns and flight-to-safety), with implications for monetary and exchange rate management.

### Methodology and data
- Modeling framework: AR-GARCH specification for forex returns and conditional variance, following Engel (1982) and Bollerslev (1986).
- Return equation (as specified):
  - Exchange rate return: dlx_t = φ_0 + ∑_{i=1}^m φ_i dlx_{t-1} + ∑_{i=1}^n θ_i z_{it} + ∑_{i=1}^k π_i Ω_{it} + ε_t
  - ε_t = σ_t^{1/2} η_t, η_t ~ i.i.d. (0, 1).
- Conditional variance specification:
  - σ_t^2 = α_0 + α_1 ε_{t-1}^2 + β_1 σ_{t-1}^2
- Long-run elasticity of forex returns to mature market volatility: ∑_{i=1}^k π_i / (1 – ∑_{i=1}^m φ_i).
- Requirements for well-defined variance: α_0, α_1, β_1 ≥ 0 and α_1 + β_1 < 1 for finite unconditional variance α_0/(1–α_1–β_1).
- Mature market volatility proxies:
  - VIX (CBOE volatility index, forward-looking for S&P500).
  - VDAX (implied volatility of the DAX, 30-day DAX option contracts).
- Euro and yen forex returns included as regressors to proxy global developments. Interest rate differentials not explicitly included (assumed proxied by lagged forex returns).

### Pre-estimation diagnostics
- Log exchange rate series (lx_t) were I(1); first differences I(0). VIX index I(1).
- AIC suggested two lags of dependent variable and regressors in estimation equations.
- Granger causality tests did not reject the null that VIX does not Granger cause East Asian exchange rates.
- Squared returns showed persistence/clustering; ARCH tests supported GARCH formulation.
- Error distributions were skewed and leptokurtic → nonnormal errors; generalized exponential distribution (GED) used for errors (GED parameter fixed at 1.5).

### GARCH estimation specifications
- Baseline models: AR(2)-GARCH(1,1) with VIX (and separately VDAX) as regressors.
- Error distribution: generalized error distribution (GED).
- Included observations (VIX models): 1822 after adjustments; GED parameter fixed at 1.5.
- Significance: coefficients on VIX were highly significant in all VIX-based models; conditional variance coefficients (α_1, β_1) significant and nonnegative in all cases with α_1 + β_1 < 1.

### Empirical results — sensitivity of forex returns to mature equity market volatility
- Main finding: increase in mature market equity volatility associated with lower forex returns (exchange rate depreciation) for all five East Asian economies — evidence of a “flight-to-safety” effect.
- Reported range of long-run elasticities of East Asian forex returns to mature equity market volatility: 0.03 to 0.1.
  - Interpretation provided: a 5 percentage point increase in the VIX index was associated, on average, with 0.15–0.4 percentage point exchange rate depreciation.
- Cross-country ordering of sensitivity (text summary): IDN at the higher end; KOR and SGP middle; PHL and THA lower.
- VIX_GARCH model coefficient summary (Sample period: 2001-07) reported in the paper:
  - VIX: IDN -0.08; KOR -0.06; PHL -0.03; SGP -0.04; THA -0.03
  - Euro/$: IDN 0.07; KOR 0.14; PHL 0.02; SGP 0.08; THA 0.07
  - Yen/$: IDN 0.04; KOR 0.13; PHL 0.03; SGP 0.00; THA 0.00

### Volatility: conditional and unconditional measures
- Unconditional variances and standard deviations from VIX_GARCH models (Sample period: 2001-07):
  - Unconditional Variance: IDN 1.00; KOR 0.14; PHL 0.12; SGP 0.07; THA 0.09
  - Unconditional SD: IDN 1.00; KOR 0.37; PHL 0.34; SGP 0.27; THA 0.30
- Patterns:
  - For KOR, SGP, and THA, conditional volatilities converge toward unconditional volatilities with episodes of “excess” volatility followed by moderation.
  - For PHL and IDN (especially IDN), elevated conditional volatility early in the sample biased unconditional volatility upward.
- Subsample analysis: two subsamples defined:
  - 2001–2003Q2 (generally elevated VIX/VDAX)
  - 2003Q3–07 (more moderate VIX/VDAX)
- VIX_GARCH subsample results (selected figures reported):
  - Sample period: 2001-03Q2 — VIX elasticities: IDN -0.04; KOR -0.03; PHL 0.00; SGP -0.03; THA -0.03
    - Unconditional Variance (where reported): KOR 0.21; PHL 0.23; SGP 0.08; THA 0.07
    - Unconditional SD: KOR 0.45; PHL 0.48; SGP 0.28; THA 0.27
  - Sample period: 2003Q3-07 — VIX elasticities: IDN -0.09; KOR -0.08; PHL -0.05; SGP -0.05; THA -0.02
    - Unconditional Variance: IDN 0.25; KOR 0.11; PHL 0.13; SGP 0.06; THA 0.24
    - Unconditional SD: IDN 0.50; KOR 0.33; PHL 0.36; SGP 0.25; THA 0.49

### Stylized facts from subsamples and interpretation
- General result holds: higher mature market volatility → depreciation of East Asian currencies (flight-to-safety).
- Elasticities generally higher during the latter subsample (2003Q3–07), possibly reflecting greater integration of East Asian asset markets into the global economy.
- Elasticities remained negative during 2006–07 and increased in magnitude for some countries (especially the Philippines), indicating exposure to subprime-related “fears.”
- Long-run exchange rate volatility tended to be higher in the earlier subsample, potentially reflecting post-Asian-crisis effects and initial experiences with flexible exchange rates; long-run volatility appears to have fallen as fundamentals strengthened and markets acclimatized to new regimes.
- Country-specific notes:
  - IDN experienced the highest forex volatility among sample countries.
  - SGP measured the lowest volatility, partly due to tighter exchange rate management.
  - KOR and SGP exhibited steady conditional and unconditional volatility.
  - PHL: unconditional volatility fell in the latter subsample, but conditional volatility rose.
  - THA: increase in unconditional and conditional volatility, partly related to political uncertainties in 2006.

### Robustness checks
- VDAX substituted for VIX (high correlation between VIX and VDAX: correlation coefficient 0.88). VDAX was more volatile than VIX over the sample.
- VDAX-based GARCH estimates: broadly similar results; long-run elasticities to VDAX generally a bit smaller than to VIX; unconditional variances and standard deviations differences negligible.
- VDAX_GARCH models (Sample period: 2001–07) — reported figures:
  - VDAX elasticities: IDN -0.06; KOR -0.07; PHL -0.02; SGP -0.02; THA -0.02
  - Unconditional Variance: IDN 0.97; KOR 0.14; PHL 0.13; SGP 0.07; THA 0.10
  - Unconditional SD: IDN 0.99; KOR 0.37; PHL 0.36; SGP 0.27; THA 0.31
- Additional robustness: alternative lag lengths (one lag for KOR, PHL, SGP, THA; three for IDN) produced nearly the same parameter estimates for VDAX elasticities and unconditional moments.
- VDAX subsample results (selected):
  - Sample period: 2001-03Q2 — VDAX elasticities: IDN -0.02; KOR -0.05; PHL -0.00; SGP -0.02; THA -0.02
    - Unconditional Variance (IDN reported separately): IDN 7.98; KOR 0.20; PHL 0.28; SGP 0.08; THA 0.07
    - Unconditional SD: IDN 2.82; KOR 0.45; PHL 0.53; SGP 0.28; THA 0.27
  - Sample period: 2003Q3-07 — VDAX elasticities: IDN -0.09; KOR -0.08; PHL -0.04; SGP -0.04; THA -0.02
    - Unconditional Variance: IDN 0.25; KOR 0.11; PHL 0.13; SGP 0.07; THA 0.31
    - Unconditional SD: IDN 0.50; KOR 0.33; PHL 0.36; SGP 0.26; THA 0.56

### Conclusions — key takeaways
- During 2001–07, forex returns for Indonesia, Korea, Philippines, Singapore, and Thailand declined when mature market equity volatility rose — consistent with a “flight-to-safety” effect.
- GARCH estimates suggest that a 5 percentage point increase in mature market equity volatility was associated with an exchange rate depreciation of up to ½ percent.
- Sensitivity of East Asian exchange rates to mature market volatility rose during the later sample period, suggesting greater global integration.
- Estimated GARCH models provide unconditional standard deviations as operational measures of “long-term” and “excess” volatility; a key finding is that long-run forex volatility declined over the sample, possibly reflecting stronger fundamentals and adaptation to more flexible regimes alongside lower mature market volatility.

*Source: _wp08208 - References (PDF chapter/section, sample content pages 3–31).*

### References

### _wp08208 - References

### References

- Ahoniemi, K., 2006, Modeling and Forecasting Implied Volatility—An Econometric Analysis of the VIX Index, Helsinki Center for Economic Research Discussion Paper 129 (Finland; Helsinki: University of Helsinki).

- Anderson, T.G, T. Bollerslev, P. Christophersen, and F. Diebold, 2006, Volatility and Correlation Forecasting, in G. Elliot, et. al., Handbook of Economic Forecasting (Massachusetts; Burmington: Elsevier Publications).

- Bollerslev, T. (1986), Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 31.

- Cairns, J., C. Ho, and R. McCauley, 2007, “Exchange Rate and Global Volatility: Implications for Asia-Pacific Currencies,” BIS Quarterly Review (March).

- Engle, R. F., 1982, Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom inflation, Econometrica, 50.

- Ho, C., G. Ma, and R. McCauley, 2005, “Trading Asian Currencies,” BIS Quarterly Review (March).

- Mills, T. C., The Econometric Modeling of Financial Time Series, 1999.

- Nelson, D. B., 1991, Conditional Heteroskedasticity in Asset Returns, Econometrica, 59.

*Source: _wp08208 - References*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08208.pdf_