The model-free implied volatility (MFVOL) has gained notoriety in recent years, partially due to the Chicago Board Option Exchange (CBOE) publication of the VIX index which is based on the MFVOL. This volatility measure extracts the expected future return volatility from the full cross-section of options with different strikes for a given maturity date. Conceptually, the MFVOL provides the market price of future volatility. If there is a volatility risk premium, the MFVOL will deviate systematically from the future realized return volatility. This is the case for the VIX, as it overstates the subsequent volatility by a large margin on average. This implies that exposure to S&P 500 volatility carries a negative risk premium. Intuitively, investors are willing to pay high prices for the insurance against spikes in the market volatility. In this paper, we refine the analysis of the volatility risk premium in many dimensions. We exploit the concept of corridor implied volatility to break the MFVOL into slices representing the pricing of market volatility over different intervals for the underlying asset price. One, we study the size of the volatility risk premium for drops versus increases in the underlying asset price. Two, we extract the premium for volatility risk in the tails of the risk-neutral price density. Three, we explore asset classes beyond the broad equity market, in particular, foreign exchange markets. Four, we develop conditional measures of the time-variation in the relative pricing of risk in up- and down-states. This down-up-ratio (DUR) provides a gauge on the shifts in the pricing of volatility on the downside versus the upside. Our findings suggest that the DUR is highly correlated with the overall risk aversion in the market and thus provides a theoretically motivated summary statistic which speaks to the time-variation in the pricing of market risks more generally.
|Original language||English (US)|
|Number of pages||39|
|State||Published - May 2009|
- Model-free implied volatility
- Barrier implied volatility
- Realized volatility
- Risk-neutral density