In this paper, we present a generic framework known as the minimal partial proxy simulation scheme. This framework allows for a stable computation of the Monte-Carlo Greeks for financial products with trigger features via finite difference approximation. The minimal partial proxy simulation...

We demonstrate how to compute first- and second-order sensitivities of portfolio credit derivatives such as synthetic collateralized debt obligation (CDO) tranches using algorithmic Hessian methods developed in Joshi and Yang (2010) in a single-factor Gaussian copula model. Our method is correct...

We discuss the issues involved in an efficient computation of the price and sensitivities of Bermudan exotic interest rate derivatives in the cross-currency displaced diffusion LIBOR market model. Improvements recently developed for an efficient implementation of the displaced diffusion LIBOR...

We first develop an efficient algorithm to compute Deltas of interest rate derivatives for a number of standard market models. The computational complexity of the algorithms is shown to be proportional to the number of rates times the number of factors per step. We then show how to extend the...

We incorporate a simple and effective control-variate into Fourier inversion formulas for vanilla option prices. The control-variate used in this paper is the Black-Scholes formula whose volatility parameter is determined in a generic non-arbitrary fashion. We analyze contour dependence both in...

We present a new non-nested approach to computing additive upper bounds for callable derivatives using Monte Carlo simulation. It relies on the regression of Greeks computed using adjoint methods. We also show that it is is possible to early terminate paths once points of optimal exercise have...

We introduce a new approach to computing sensitivities of discontinuous integrals. The methodology is generic in that it only requires knowledge of the simulation scheme and the location of the integrand's singularities. The methodology is proven to be optimal in terms of minimizing the variance...

In this paper, we present an efficient approach to compute the first and the second order price sensitivities in the Heston model using the algorithmic differentiation approach. Issues related to the applicability of the pathwise method are discussed in this paper as most existing numerical...

Credit value adjustment (CVA) and related charges have emerged as important risk factors following the Global Financial Crisis. These charges depend on uncertain future values of underlying products, and are usually computed by Monte Carlo simulation. For products that cannot be valued...

The calculation of prices and sensitivities of exotic interest rate derivatives in the LIBOR market model is often very time consuming. One approach that has been previously suggested is to use a Markov-functional model as a control variate for prices and deltas but not vegas. We present a new...