Heston PDE Derivation

Quant Researcher · Stochastic Calculus

Question

Derive the Heston PDE from the multidimensional Itô lemma applied to

V(t, S, \nu)

where

dS = \sqrt{\nu}\,S\,dW^1

and

d\nu = \kappa(\bar{\nu} - \nu)\,dt + \xi\sqrt{\nu}\,dW^2

, with

d\langle W^1, W^2 \rangle = \rho\,dt

. Identify the cross-derivative term and explain its role in generating the implied vol skew.

8 / 10