Abstract

http://ssrn.com/abstract=1718102
 
 

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First and Second Order Greeks in the Heston Model


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

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.

Number of Pages in PDF File: 33

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

JEL Classification: G13

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Date posted: December 2, 2010 ; Last revised: September 5, 2014

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: http://ssrn.com/abstract=1718102 or http://dx.doi.org/10.2139/ssrn.1718102

Contact Information

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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