Study on option pricing in an incomplete market with stochastic volatility based on risk premium analysis

We focus on an option pricing mechanism in a market, for which the underlying asset has a stochastic volatility. This model generally belongs to the class of incomplete market models, and hence, a no-arbitrage option price is not uniquely determined. However, in the actual market, options are traded at some price. This fact may suggest that the market participant compromises on the risk caused by stochastic volatility and that the balance of risk aversion of sellers and buyers determines the market price. To analyze this mechanism, we introduce a concept of the risk premium for stochastic volatility (RPSV) and develop a method to estimate the RPSV implied in actual option prices. In the method, homogeneous RPSV is not required to allow the segmentation of the market. Estimated RPSV of Nikkei 225 options are almost positive, and certainly depend on the strike price and time to maturity.