Optimal Partial Proxy Method for Computing Gammas of Financial Products with Discontinuous and Angular Payoffs
28 Pages Posted: 3 May 2014
Date Written: May 1, 2014
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
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