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First and Second Order Greeks in the Heston Model

33 Pages Posted: 2 Dec 2010 Last revised: 5 Sep 2014

Jiun Hong Chan

University of Melbourne - Centre for Actuarial Studies

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies

Dan Zhu

University of Melbourne - Centre for Actuarial Studies

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Date Written: December 26, 2010

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.

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

JEL Classification: G13

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

Jiun Hong Chan

University of Melbourne - Centre for Actuarial Studies ( email )

Melbourne, 3010
Australia

Mark Joshi (Contact Author)

University of Melbourne - Centre for Actuarial Studies ( email )

Melbourne, 3010
Australia

Dan Zhu

University of Melbourne - Centre for Actuarial Studies ( email )

Melbourne, 3010
Australia

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