Negative Volatility Risk Premium Research Articles

Performance expectations of basic options strategies may be different than you think

There is much empirical evidence for the existence of a negative volatility risk premium. We consider how the volatility risk premium affects the returns of portfolios implementing seven popular option strategies. We find that option selling generates substantial excess return as well as risk mitigation by providing short exposure to the volatility risk premium. Net option buying is able to protect against extreme losses; however, these losses are very infrequent and short lived. Even during these periods, the long net exposure to the volatility risk premium erodes protection as the depth and duration of the losses persist.

Performance Expectations of Basic Options Strategies May Be Different Than You Think

There is much empirical evidence for the existence of a negative volatility risk premium. We consider how the volatility risk premium affects the returns of portfolios implementing seven popular option strategies. We find that option selling generates substantial excess return as well as risk mitigation by providing short exposure to the volatility risk premium. Net option buying is able to protect against extreme losses, however, these losses are very infrequent and short lived. Even during these periods, the long net exposure to the volatility risk premium erodes protection as the depth and duration of the losses persist.

Delta-hedged gains and risk-neutral moments

We investigate the well-documented underperformance of delta-hedged option portfolios in relation to ex ante moments of the stock market's return distribution. Using a sample of Standard and Poor's 500 index options, we find that delta-hedged option gains decrease with ex ante volatility, in support of a negative volatility risk premium. Moreover, the delta-hedged gains are negatively associated with skewness and kurtosis of call options, but positively associated with the higher moments of put options. These results suggest that investors pay a premium for call options in anticipation of a positive jump, while they pay a premium for put options in anticipation of a negative jump.

Implied risk aversion and volatility risk premiums

Since investor risk aversion determines the premium required for bearing risk, a comparison thereof provides evidence of the different structure of risk premium across markets. This article estimates and compares the degree of risk aversion of three actively traded options markets: the S&P 500, Nikkei 225 and KOSPI 200 options markets. The estimated risk aversions is found to follow S&P 500, Nikkei 225 and KOSPI 200 options in descending order, implying that S&P 500 investors require more compensation than other investors for bearing the same risk. To prove this empirically, we examine the effect of risk aversion on volatility risk premium, using delta-hedged gains. Since more risk-averse investors are willing to pay higher premiums for bearing volatility risk, greater risk averseness can result in a severe negative volatility risk premium, which is usually understood as hedging demands against the underlying asset's downward movement. Our findings support the argument that S&P 500 investors with higher r...

Negative Market Volatility Risk Premium: Evidence from the LIFFE Equity Index Options*

AbstractWe provide non‐parametric empirical evidence regarding negative volatility risk premium using LIFFE equity index options. In addition, we incorporate the moment‐adjusted option delta hedge ratio to mitigate the effect of model misspecification. From the results, we observe several interesting phenomena. First, the delta‐hedged gains are negative. Second, with a correction for model misspecification, higher‐order moments measures show less significance and the volatility risk premium still plays a key role in affecting delta‐hedged gains. All empirical evidence supports the existence of negative volatility risk premium in LIFFE equity index options.

Is volatility risk priced in the KOSPI 200 index options market?

AbstractThe negative volatility risk premium is understood as a result for a hedging demand against market declines. Although this negative volatility risk premium is observed in most index options markets, there are some doubts about its presence in the KOSPI 200 index options market. The majority of KOSPI 200 index option holders do not possess any position in the underlying market; the composition of trading groups of the KOSPI 200 index options significantly differs from that of its underlying index; in this circumstance, the presence of a hedging demand is questionable. This study shows that volatility risk does not require a premium in the KOSPI 200 index options market. Rather, jump fears influence KOSPI 200 options. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 29:797–825, 2009

The Volatility Risk Premium in the KOSPI200 Index Options

This study examines whether the volatility risk premium is reflected on the prices of the KOSPI200 index options. By applying the empirical method of Bakshi and Kapadia (2003), we analyze the performance of delta-hedging strategy in the KOSPI200 index market. They showed the existence of the negative volatility risk premium in the S&P 500 index options as well as derived theoretical positive relationship between the volatility risk premium and delta-hedging gains. However, in the results of this study, contrary to those in the S&P 500 index options market, we do not observe the volatility risk premium. Delta-hedged gains of ATM options are not significantly negative. Delta-hedged gains are not more negative as historical volatility increases and as options' vega and remaining maturity increase. However, the notable finding of this study is that delta-hedged gains of OTM options and put options are negative and signigicant. This results can be caused by the phenomenon of overpriced puts or by market microstructure factors, such as relatively wide bid-ask spread and high tick size. In a simple examination of comparison between changes in traded option prices and changes in the Black-Scholes option prices during delta-hedging period, negative delta-hedged gains seem to be attributed to too small changes in call option prices and too large changes in put option prices. In conclusion, by analyzing the delta-hedged gains, the volatility risk risk premium seems not be observed in the KOSPI200 index options market.

The Cross-Section of Average Delta-Hedge Option Returns Under Stochastic Volatility

Existing evidence indicates that average returns of purchased market-hedge S&P 500 index calls, puts, and straddles are non-zero but large and negative, which implies that options are expensive. This result is intuitively explained by means of volatility risk and a negative volatility risk premium, but there is a recent surge of empirical and analytical studies which also attempt to find the sources of this premium. An important question in the line of a priced volatility explanation is if a standard stochastic volatility model can also explain the cross-sectional findings of these empirical studies. The answer is fairly positive. The volatility elasticity of calls and puts is several times the level of market volatility, depending on moneyness and maturity, and implies a rich cross-section of negative average option returns -- even if volatility risk is not priced heavily, albeit negative. We introduce and calibrate a new measure of option overprice to explain these results. This measure is robust to jump risk if jumps are not priced.

Identifying volatility risk premia from fixed income Asian options

Fixed income options are frequently adopted by companies to hedge interest rate risk. Their payoff dependence on the cumulative short-term rate makes them particularly informative about interest rate volatility risk. Based on a joint dataset of bonds and Asian interest rate options, we study the interrelations between bond and volatility risk premia in a major emerging fixed income market. We propose a dynamic term structure model that generates an incomplete market compatible with a preliminary empirical analysis of the dataset. Approximation formulas for at-the-money Asian option prices avoid the use of computationally intensive Fourier transform methods, allowing for an efficient implementation of the model. The model generates a bond risk premium strongly correlated with a widely accepted emerging market benchmark index (EMBI-Global), and a negative volatility risk premium, consistent with the use of Asian options as insurance in this market.

The cross-section of average delta-hedge option returns under stochastic volatility

Existing evidence indicates that average returns of purchased market-hedge S&P 500 index calls, puts, and straddles are non-zero but large and negative, which implies that options are expensive. This result is intuitively explained by means of volatility risk and a negative volatility risk premium, but there is a recent surge of empirical and analytical studies which also attempt to find the sources of this premium. An important question in the line of a priced volatility explanation is if a standard stochastic volatility model can also explain the cross-sectional findings of these empirical studies. The answer is fairly positive. The volatility elasticity of calls and puts is several times the level of market volatility, depending on moneyness and maturity, and implies a rich cross-section of negative average option returns—even if volatility risk is not priced heavily, albeit negative. We introduce and calibrate a new measure of option overprice to explain these results. This measure is robust to jump risk if jumps are not priced.

Identifying Volatility Risk Premia from Fixed Income Asian Options

Fixed income Asian options are frequently adopted by companies to hedge interest rate risk. Having a payoff structure depending on the cumulative short-term rate makes them particularly informative about interest rate volatility risk. Based on a joint dataset of bonds and Asian interest rate options, we study the inter-relations between bond and volatility risk premiums in a major emerging fixed income market. We propose and implement a dynamic term structure model that generates an incomplete market, compatible with a preliminary empirical analysis of the dataset. Approximation formulas for at-the-money Asian option prices avoid the use of computationally intensive Fourier transform methods, allowing for an efficient implementation of the model. The model generates bond risk premium strongly correlated (89%) with a widely accepted emerging market benchmark index (EMBI-Global), and a negative volatility risk premium, consistent with the use of Asian options as insurance in this market. Volatility premium explains a significant portion (33%) of bond premium, indicating that the Asian options market considerably affects the prices of risk of its neighbor bond market.

A Study on the Return Dynamics using the Implied Information

This article empirically analyzes some properties by all one-dimensional diffusion option models by using the martingale restriction test and examines the systematic risk factors Implied In return dynamics of KOSPI 200 index options. We find that the martingale restriction under one-dimensional diffusion option model is strongly rejected by the data because of the negative volatility risk premium. Therefore options are not redundant securities, nor monotonically increasing (decreasing) in the underlying asset price and also option prices are not perfectly correlated with each other and with the underlying asset. And under the non-complete of the market. the informational led-lag relationship between the stock indices and the stock index options exist.

On the Negative Market Volatility Risk-Premium: Bridging the Gap Between Option Returns and the Pricing of Options

Existing evidence indicates that (i) average returns of purchased delta-hedged options are negative, implying options are expensive, and (ii) volatility is the most important extra risk that is factored into option prices. Therefore, a natural extension is to explain the cross-section of average delta-hedged option returns in a stochastic volatility model. This paper solves this problem by introducing a measure of option overprice, which quantifies the impact on option prices of the volatility risk premium. It is an application of option-pricing in incomplete markets under stochastic volatility. An extensive numerical exercise shows the option overprice is consistent with the cross-section of average delta-hedged returns of calls, puts, and straddles reported by the literature for the S&P 500 index, except for expensive short-term out-of-the-money puts. In a stochastic volatility model, the volatility risk of at- and, especially, out-of-the-money calls and puts is several times larger than market volatility, which explains large negative volatility risk premiums if volatility risk is negative priced.