First- and Second-Order Greeks in the Heston Model

52 Pages Posted: 24 Jun 2016

See all articles by Jiun Hong Chan

Jiun Hong Chan

University of Melbourne - Centre for Actuarial Studies

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies (deceased)

Dan Zhu

Monash University - Department of Econometrics & Business Statistics

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Date Written: April 20, 2015

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.

Keywords: Heston stochastic volatility, first- and second-order Greeks, algorithmic differentiation, simulation schemes, numerical methods

Suggested Citation

Chan, Jiun Hong and Joshi, Mark and Zhu, Dan, First- and Second-Order Greeks in the Heston Model (April 20, 2015). Journal of Risk, Vol. 17, No. 4, 2015, Available at SSRN: https://ssrn.com/abstract=2799662

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 (deceased) ( email )

Melbourne, 3010
Australia

Dan Zhu

Monash University - Department of Econometrics & Business Statistics ( email )

Wellington Road
Clayton, Victoria 3168
Australia

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