Implied Volatility in Heston Model

Question

recently I started reading the interesting book about option pricing in the stochastic volatility world from Lewis. He gives very interesting and detailed insights about this topic in general. However the book does not cover the implied volatility topic. That's why I am interested of how I get implied volatility out of the Heston Model. Do I have to calculate an european call price with Heston's formula and then reverse it by the help of Black Scholes to get the implied volatility?

Thanks in advance

Answer 1

The option price with a Heston volatility model depends on the Heston parameters only. That is, the implied volatility parameters does not enter into the Heston option price formula. Unless there is an analytical formula to compute the implied volatility for a given option price, it is impossible to compute the implied volatility directly from the Heston parameters. What people usually do is to first compute the European option, from the Heston volatility process, using either Fourier transformation or Monte Carlo, and then compute the implied volatility using the Newton's method or the bi-section method.