First- and second-order Greeks in the Heston model

Jiun Hong Chan, Mark Joshi, Dan Zhu

Research output: Contribution to journalArticleResearchpeer-review

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.
LanguageEnglish
Pages19-69
Number of pages51
JournalJournal of Risk
Volume17
Issue number4
DOIs
Publication statusPublished - 2015
Externally publishedYes

Keywords

  • Heston process
  • stochastic volatility
  • Greeks

Cite this

Chan, Jiun Hong ; Joshi, Mark ; Zhu, Dan. / First- and second-order Greeks in the Heston model. In: Journal of Risk. 2015 ; Vol. 17, No. 4. pp. 19-69.
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First- and second-order Greeks in the Heston model. / Chan, Jiun Hong; Joshi, Mark; Zhu, Dan.

In: Journal of Risk, Vol. 17, No. 4, 2015, p. 19-69.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Joshi, Mark

AU - Zhu, Dan

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AB - 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.

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KW - stochastic volatility

KW - Greeks

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