On the pricing of forward starting options in Heston’s model on stochastic volatility

We consider the problem of pricing European forward starting options in the presence of stochastic volatility. By performing a change of measure using the asset price at the time of strike determination as a numeraire, we derive a closed-form solution within Heston’s stochastic volatility framework applying distribution properties of the volatility process. In this paper we develop a new and more suitable formula for pricing forward starting options. This formula allows to cover the smile effects observed in a Black-Scholes environment, in which the extreme exposure of forward starting options to volatility changes is ignored.