Computations of Greeks in stochastic volatility models via the Malliavin calculus

The application of the Malliavin calculus to the computations of price sensitivities were introduced by [1] for models with deterministic volatility. In this work, we compute the Greeks, for stochastic volatility models where the underlying asset price is driven by Brownian information. We consider stochastic volatility models, since these models, unlike those with deterministic volatility, take into account the smile effect. Let (Bt)t∈[0,T ] and (B ′ t)t∈[0,T ] be two independent Brownian motions. We work in a filtered probability space (Ω,F , (Ft)t∈[0,T ], P ), where (Ft)t∈[0,T ] is the naturel filtration generated by B and B ′ . We consider a market with two assets, a riskless one with price (e R