Alternative form of analytic solution of European option price in model with stochastic volatility driven by Ornstein-Uhlenbeck process using bilateral Laplace transform

Abstract

Bilateral Laplace transform is known for its capability on taking Laplace transform over all real numbers. This paper provides a different approach by using inverse bilateral Laplace transform on deriving analytic solution of European option price formula, both call option and put option. Case of uncorrelated processes between asset price and volatility of Black-Scholes model of asset pricing with stochastic volatility driven by Ornstein-Uhlenbeck process is used to portray price of a risky asset in the market. This paper also provides proof for required formulations to derive the analytic solutions and reference for alternative forms of inverse bilateral Laplace transform.