First- and second-order Greeks in the Heston model

Jiun Hong Chan, Mark Joshi and Dan Zhu

Abstract

Abstract

We present an efficient approach to compute the first- and second-order price sensitivities in the Heston model using algorithmic differentiation. Issues related to the applicability of the pathwise method are discussed in this paper as most existing numerical schemes are not Lipschitz continuous 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 distributions while price sensitivities obtained using the integrated double gamma scheme and the double gamma scheme remain stable.