Pricing Geometric Asian Options under Stochastic Volatility Framework

摘要

Option pricing problem plays an extremely important role in quantitative finance. In complete market, Black-Scholes-Merton theory has been central to the development of financial engineering as both discipline and profession. However, in an incomplete market, there isn't any replicating portfolios for those options, and thus, we cannot apply the law of one price in order to obtain a unique solution. Fortunately, we can get a fair price via local-equilibrium principle. In this paper, we develop Dennis Yang's theory to price the exotic option-Geometric Asian option, and analysis the relationship of the price and the current position. We get the explicit expression for the market price of the risk (followed Dennis Yang, we call it personal price of the risk on Asian options). The position effect plays a significant role on option pricing, because it can tell the trader how many and which direction to trade with the market in order to reach the local equilibrium with the market.