Option prices under stochastic volatility

The well known Heston model for stochastic volatility captures the reality of the motion of stock prices in our financial market. However, the solution of this model is expressed as integrals in the complex plane and has difficulties in numerical evaluation. Here, we present closed-form solutions for option prices and implied volatilities in terms of series expansions. We show that our theoretical predictions are in remarkably good agreement with numerical solutions of the Heston model of stochastic volatility.