N., E. Platen and M. Schweizer
Title: Option Pricing under Incompleteness and Stochastic Volatility
Abstract: We consider a very general diffusion model for asset prices which allows the description of stochastic and past-dependent volatilities. Since this model typically yields an incomplete market, we show that for the purpose of pricing options, a small investor should use the minimal equivalent martingale measure associated to the underlying stock price process. Then we present stochastic numerical methods permitting the explicit computation of option prices and hedging strategies, and we illustrate our approach by specific examples.
Keywords: option pricing, stochastic volatility, incomplete markets, equivalent martingale measures, stochastic numerical methods
Creation-Date: February 1992
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