Closed Form Convexity and Cross-Convexity Adjustments for Heston Prices
Quantitative Finance, Vol. 11, No. 8, 2011
27 Pages Posted: 4 Apr 2009 Last revised: 30 Jul 2011
Date Written: October 1, 2009
We present a new and general technique for obtaining closed form expansions for prices of options in the Heston model, in terms of Black-Scholes prices and Black-Scholes greeks up to arbitrary orders. We then apply the technique to solve, in detail, the cases for the second order and third order expansions. In particular, such expansions show how the convexity in volatility, measured by the Black-Scholes volga, and the sensitivity of delta with respect to volatility, measured by the Black-Scholes vanna, impact option prices in the Heston model. The general method for obtaining the expansion rests on the construction of a set of new probability measures, equivalent to the original pricing measure, and which retain the affine structure of the Heston volatility diffusion. Finally, we extend our method to the pricing of forward-starting options in the Heston model.
Keywords: stochastic volatility, Heston model, price approximation, forward starting options, forward skew, forward smile
JEL Classification: C63, G13
Suggested Citation: Suggested Citation