Is Stochastic Volatility always Priced on Index Options?

Abstract

The negative volatility risk premium implied on index options is a common concept to explain the difference of the historical volatility and the implied volatility. Since the volatility of an underlying index becomes higher as the market moves down, holding both an underlying asset and the option induces a hedging effect against significant market declines. In a circumstance, however, in which each market is dominated by different investors, such an explanation may not be reliable anymore. This study proves the argument via KOSPI 200 index options. The KOSPI 200 index market is mainly driven by institutional investors and foreign investors, whereas its related options market is dominated by individual investors. We shows that the volatility risk is not priced on KOSPI 200 index option, using the delta-hedged gains on a portfolio of a long position in a call, hedged by a short position in the underlying asset (Bakshi and Kapadia (2003)). Rather, jump fear influences in determining KOSPI 200 option prices. The results are consistent with extant literatures that have shown that the Korean derivatives market is dominated by directional traders, thus questioning the existence of hedging demands on option trades. In this research, no specifications are imposed on the stochastic processes of the underlying asset, volatility, and jumps, consequently freeing the results from misspecification errors.