Prices Expansion in the Wishart Model

Abstract:     
Using probability change techniques introduced by Drimus for Heston model, the paper derives a nth order expansion formula of Wishart option price in terms of Black-Scholes price and Black-Scholes Greeks. Numerical results are given for the second-order case. Due to this new approximation, the smile implied by the Wishart model can be better understood. The sensitivity of Delta and Vega to the volatility (Vanna and Volga respectively) indeed appears explicitly in this formula. En route to this formula, the paper presents a number of new results on Laplace transforms and moments of the integrated Wishart processes.

Keywords: stochastic volatility, wishart model, price approximation, stochastic correlation, probability change

Accepted Paper Series