Optimal Partial Proxy Method for Computing Gammas of Financial Products with Discontinuous and Angular Payoffs. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Joshi, Mark S.; Zhu, Dan
• Is Part Of: Applied mathematical finance. Volume 23:Issue 1(2016)
• Page Start: 22
• Page End: 56
• Publication Date: 2016-01-02
• Subjects: Greeks -- Monte Carlo simulation -- derivatives pricing -- Hessian -- Gamma; Business mathematics -- Periodicals; 650.0151
• DOI: 10.1080/1350486X.2016.1156487
• Languages: English
• ISSNs: 1350-486X

Abstract

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.