First and Second Order Greeks in the Heston Model

Abstract:     
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.

Number of Pages in PDF File: 28

Keywords: Heston, Stochastic Volatility, Hessian Greeks, Monte Carlo Simulation, Algorithmic Differentiation

JEL Classification: G13

working papers series