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...

The problem of estimating expectations of functions of conditional expectations using nested Monte Carlo simulation is studied. It is shown that typically the bias arising from non-linearity is in leading order inversely proportional to the number of sub-simulation paths when using a naive...

Infinitesimal perturbation analysis is a widely used approach to assess the input sensitivities of stochas- tic dynamic systems in the classical simulation context. In this paper, we introduce an efficient nu- merical approach to undertake Infinitesimal perturbation analysis in the context of...

We compute first and second-order sensitivities of functions simulated by rejection techniques. The methodology is to perform a measure change on every acceptance test, so that the pathwise discontinuities resulting from the rejection decisions are removed. The change of measure is chosen to be...

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...

Prudential regulations require financial institutions to hold initial capital so that the possibility of ruin is very low. An important practical problem is to estimate the regulatory capital so the ruin probability is at the regulatory level, typically less than 0.1% over a finite-time horizon....

We introduce a new simulation algorithm for computing the Hessians of Bermudan swaptions and cancellable swaps, the resulting pathwise estimates are unbiased and accurate. Given the exercise strategy, the pathwise angularities are removed by a sequence of measure changes. The change of measure...

Bayesian inference relies heavily on numerical Markov chain Monte carlo (MCMC) methods for the estimation of the typically intractable high-dimensional posterior distributions and requires specific inputs. In this paper we introduce a new general and efficient numerical approach to address...