An Actuarial Approach to Option Pricing under O-U Process and Stochastic Interest Rates

This paper discusses an actuarial approach to the option pricing problem for a market model where the interest rates are stochastic and the stock prices are driven by generalized Exp-Ornstein-Uhlenback process. According to the definition of actuarial pricing approach, the exact solutions of the general European option and the exchange option are obtained with the help of related theory of stochastic differential equation. Then the European call-put parity relation is derived naturally. Furthermore, the new prices of European call option and the put option with continuous dividend yield are deduced from the above results. At last, a comparative analysis of numerical simulation is made between the above-mentioned results and the B-S pricing formula. All the results are applicable to complex incomplete markets.