Knightian uncertainty based option pricing with stochastic volatility

This paper deals with the stochastic volatility option pricing model in the viewpoint of Knightian uncertainty. First, we prove that the stochastic volatility model is in fact a Knightian uncertainty model; and we use the discounted relative entropy to measure the Knighitan uncertainty. Then, having balanced the Knightian uncertainty and Knightian premium through a utility function, we get the optimum probability measure, and we get the price formula of European call option with Knightian aversion degree γ. We find that γ and expiration date have important effect on the price of option by Monte Carlo simulation, and we give an example to show how to estimate the values of γ.