Credit Valuation Adjustment (CVA) has become an important field as its calculation is required in Basel III, issued in 2010, in the wake of the credit crisis. Exposure, which is defined as the potential future loss on a financial contract due to a default event, is one of the key elements for...

We develop three numerical methods to solve coupled forward-backward stochastic differential equations. We propose three different discretization techniques for the forward stochastic differential equation. A theta-discretization of the time-integrands is used to arrive at schemes with...

This paper considers the problem of pricing options with early-exercise features whose pay-off depends on several sources of uncertainty. We propose a stochastic grid method for estimating the optimal exercise policy and using this policy to obtain a low-biased estimator for high-dimensional...

We construct multi-currency models with stochastic volatility and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of...

We define an equity-interest rate hybrid model in which the equity part is driven by the Heston stochastic volatility [Hes93], and the interest rate (IR) is generated by the displaced-diffusion stochastic volatility Libor Market Model [AA02]. We assume a non-zero correlation between the main...

In this article we define a multi-factor equity-interest rate hybrid model with non-zero correlation between the stock and interest rate. The equity part is modeled by the Heston model [Heston-1993] and we use a Gaussian multi-factor short rate process [Brigo,Mercurio-2007; Hull-2006]. By...

This paper describes a practical simulation-based algorithm, which we call the <I>Stochastic Grid Bundling Method </I> (SGBM) for pricing multi-dimensional Bermudan (i.e. discretely exercisable) options. The method generates a direct estimator of the option price, an optimal early-exercise policy as...</i>