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...

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 analyze the primal-dual upper bound method and prove that its bias is inversely proportional to the number of paths in sub-simulations for a large class of cases. We develop a methodology for estimating and reducing the bias. We present numerical results showing that the new technique is...

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...

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...

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...