Optimal partial proxy method for computing Gammas of financial products with discontinuous and angular payoffs

Mark S. Joshi, Dan Zhu

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We extend the limit optimal partial proxy method to compute second-order sensitivities of financial products with discontinuous or angular payoffs by Monte Carlo simulation. The methodology is optimal in terms of minimizing the variance of the likelihood ratio weight. Applications are presented for both equity and interest-rate products with discontinuous payoff structures. The first-order optimal partial proxy method is also implemented to calculate the Hessians of insurance products with angular payoffs. Numerical results are presented which demonstrate the speed and efficacy of the method.
LanguageEnglish
Pages22-56
Number of pages35
JournalApplied Mathematical Finance
Volume23
Issue number1
DOIs
Publication statusPublished - 2016

Keywords

  • Greeks
  • Monte Carlo simulation
  • derivatives pricing
  • Hessian
  • Gamma

Cite this

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abstract = "We extend the limit optimal partial proxy method to compute second-order sensitivities of financial products with discontinuous or angular payoffs by Monte Carlo simulation. The methodology is optimal in terms of minimizing the variance of the likelihood ratio weight. Applications are presented for both equity and interest-rate products with discontinuous payoff structures. The first-order optimal partial proxy method is also implemented to calculate the Hessians of insurance products with angular payoffs. Numerical results are presented which demonstrate the speed and efficacy of the method.",
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Optimal partial proxy method for computing Gammas of financial products with discontinuous and angular payoffs. / Joshi, Mark S.; Zhu, Dan.

In: Applied Mathematical Finance, Vol. 23, No. 1, 2016, p. 22-56.

Research output: Contribution to journalArticleResearchpeer-review

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AU - Joshi, Mark S.

AU - Zhu, Dan

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N2 - We extend the limit optimal partial proxy method to compute second-order sensitivities of financial products with discontinuous or angular payoffs by Monte Carlo simulation. The methodology is optimal in terms of minimizing the variance of the likelihood ratio weight. Applications are presented for both equity and interest-rate products with discontinuous payoff structures. The first-order optimal partial proxy method is also implemented to calculate the Hessians of insurance products with angular payoffs. Numerical results are presented which demonstrate the speed and efficacy of the method.

AB - We extend the limit optimal partial proxy method to compute second-order sensitivities of financial products with discontinuous or angular payoffs by Monte Carlo simulation. The methodology is optimal in terms of minimizing the variance of the likelihood ratio weight. Applications are presented for both equity and interest-rate products with discontinuous payoff structures. The first-order optimal partial proxy method is also implemented to calculate the Hessians of insurance products with angular payoffs. Numerical results are presented which demonstrate the speed and efficacy of the method.

KW - Greeks

KW - Monte Carlo simulation

KW - derivatives pricing

KW - Hessian

KW - Gamma

U2 - 10.1080/1350486X.2016.1156487

DO - 10.1080/1350486X.2016.1156487

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JO - Applied Mathematical Finance

T2 - Applied Mathematical Finance

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SN - 1350-486X

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