| We study option pricing in an incomplete market with stochas- tic volatility. We consider constant relative risk aversion (CRRA) preference. Under the power utility preference, we show that the fair price of the option depends on the ratio of the position in options holding to the wealth of the portfolio. Furthermore, we give an explicit expression for the market-price-of- risk and the optimal hedging scheme which is different from delta hedging. We derive an asymptotic expansion to explain the position dependence theory of option pricing. In addition, we show many numerical examples to illustrate various points. |
Updated 07/09/2013