## ONLINE ANNEX 1.1. OPTION-IMPLIED VOLATILITY: THE QUANTITY AND PRICE OF RISK FOR STOCKS AND BONDS

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**Canonical URL:** [ONLINE ANNEX 1.1. OPTION-IMPLIED VOLATILITY: THE QUANTITY AND PRICE OF RISK FOR STOCKS AND BONDS](https://www.imf.org/-/media/files/publications/gfsr/2018/april/ch1/pdf/annex1-1.pdf)

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### Key question and overview
- Examines whether the early-February VIX tantrum and late-March protectionism concerns reflected a higher perceived quantity of volatility risk or a higher price of volatility risk (variance risk premium, VRP).
- Core conclusion: option-implied volatility movements around the episode were driven more by higher volatility forecasts (quantity of risk) than by a persistent increase in the price of risk (VRP), implying continued willingness of market participants to sell volatility and broadly consistent with accommodative financial conditions.

### Methodology and data
- Uses asymmetric, generalized autoregressive conditional heteroscedasticity–based (A-GARCH-based) forecasts of volatility that allow volatility to increase when asset returns are negative.
- Compares VIX futures term structure through six months with A-GARCH six-month forecasts for dates bracketing the tantrum (January 29 and February 12, 2018).
- A-GARCH initial estimate sample: October 24, 2006–November 30, 2010.
- A-GARCH forecasts shown as real-time estimates with expanding four-year window (figure caption).
- A separate A-GARCH forecast for the VIX shown with an expanding window with 18 years minimum beginning January 5, 1970 (Online Annex Figure 1.1.2).
- Swaption analysis: at-the-money swaptions cube on February 12, with swap tenors ranging from 1 to 10 years and option expirations ranging from three months to five years.
- All market quotes sourced from Bloomberg; IMF staff estimates used throughout.

### Equity-market findings
- The VIX futures term structure shifted from modestly upward sloping to inverted between January 29 and February 12, 2018; A-GARCH forecasts showed a similar move.
- The A-GARCH forecast trajectory lies above VIX futures quotes, suggesting the VIX increase reflected a perceived greater quantity of risk rather than a notably higher price of risk.
- Dynamics through the weeks after the tantrum:
  - Options prices fell back in line with volatility forecasts by the end of the week of the VIX tantrum.
  - The VRP was often negative for the remainder of February and near zero in late March, indicating market participants were again willing to sell volatility in short order.
- Specific statistics reported in figure captions:
  - Sample average (latest value) of estimated variance risk premium = 2.73 (–0.02).
  - Z-score of latest variance risk premium = –0.74.
  - VIX (0.53953) and A-GARCH forecast (0.53747) shown for January 29–March 29, 2018 comparison.

### Interest-rate (swaption) findings
- Raw at-the-money swaption implied volatility quotes on February 12 (across option expiries and swap tenors) are generally lower than GARCH-based volatility forecasts for the same grid.
- The resulting swaption VRPs were often negative shortly after the VIX tantrum, especially for longer-dated options on longer-dated maturity swaps (Online Annex Figure 1.1.5).
- Swaption VRPs remained subdued through the weeks following early-February equity market tremors (Online Annex Figure 1.1.6).

### Interpretation and caveats
- Interpretation:
  - Net revisions in implied volatility across stocks and fixed-income instruments on balance reflect greater forecasts of volatility rather than sustained increases in the price of risk.
  - Low or negative VRPs are broadly consistent with accommodative financial conditions and market willingness to bear volatility risk.
- Caveats:
  - Analysis references net changes in closing quotes over a turbulent period; intraday VIX quotes were highly volatile and VRP may have spiked intraday as short sellers covered positions. Net changes suggest such episodes were short-lived.
  - The VRP estimates are unconditional and omit other potentially relevant variables (for example, volatility of volatility). The analysis does not determine whether the price of risk is “too high” or “too low” relative to fundamentals.
  - Similar caveats apply to the swaption VRP analysis; gaps between implied and forecast volatility could reflect changes in other variables not captured by this framework.

### Summary implications
- Short-term market stress in early February reflected a reassessment of expected volatility rather than a material shift in the compensation investors require to bear volatility risk.
- Both equity and interest-rate option markets showed that implied volatility increases were accompanied by forecasts of higher volatility, and VRPs quickly reverted to negative or near-zero levels, signaling available supply of volatility risk from market participants.

*Source: ONLINE ANNEX 1.1 to Chapter 1, April 2018 Global Financial Stability Report (IMF staff estimates based on Bloomberg market quotes).*

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_Source: https://www.imf.org/-/media/files/publications/gfsr/2018/april/ch1/pdf/annex1-1.pdf_