Optimal Partial Proxy Method for Computing Gammas of Financial Products with Discontinuous and Angular Payoffs

28 Pages Posted: 3 May 2014

See all articles by Mark S. Joshi

Mark S. Joshi

University of Melbourne - Centre for Actuarial Studies (deceased)

Dan Zhu

Monash University - Department of Econometrics & Business Statistics

Date Written: May 1, 2014

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 likelihood ratios terms. Applications are presented for both equity options 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.

Keywords: optimal partial proxy, Hessian, Monte Carlo simulation, TARN, Gamma matrix, automatic differentiation

Suggested Citation

Joshi, Mark and Zhu, Dan, Optimal Partial Proxy Method for Computing Gammas of Financial Products with Discontinuous and Angular Payoffs (May 1, 2014). Available at SSRN: https://ssrn.com/abstract=2431580 or http://dx.doi.org/10.2139/ssrn.2431580

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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