33 Pages Posted: 2 Dec 2010 Last revised: 5 Sep 2014
Date Written: December 26, 2010
In this paper, we present an efficient approach to compute the first and the second order price sensitivities in the Heston model using the algorithmic differentiation approach. Issues related to the applicability of the pathwise method are discussed in this paper as most existing numerical schemes are not Lipschitz in model inputs. Depending on the model inputs and the discretization step size, our numerical tests show that the sample means of price sensitivities obtained using the Lognormal scheme and the Quadratic-Exponential scheme can be highly skewed and have fat-tailed distribution while price sensitivities obtained using the Integrated Double Gamma scheme and the Double Gamma scheme remain stable.
Keywords: Heston, Stochastic Volatility, Hessian Greeks, Monte Carlo Simulation, Algorithmic Differentiation
JEL Classification: G13
Suggested Citation: Suggested Citation
Chan, Jiun Hong and Joshi, Mark S. and Zhu, Dan, First and Second Order Greeks in the Heston Model (December 26, 2010). Available at SSRN: https://ssrn.com/abstract=1718102 or http://dx.doi.org/10.2139/ssrn.1718102