Exercise 14.3.10 Consider the following processes: dS = Sdt + SdW1, d = ( ) dt + dW2, where dW1 and dW2 are Wiener processes

Exercise 14.3.10 Consider the following processes:

dS = μSdt +σ SdW1, dσ = β(σ −σ) dt +γ dW2, where dW1 and dW2 are Wiener processes with correlation ρ. Let H(S, σ, τ) be a function of S, σ, and τ . Derive its stochastic differential equation. (This process models stock price with a correlated stochastic volatility, which follows a meanreverting process.)