Efficient computation of exposure profiles on real-world and risk-neutral scenarios for Bermudan swaptions

Abstract

This paper presents a computationally efficient technique for the computation of exposure distributions at any future time under the risk-neutral and some observed real-world probability measures; these are needed for the computation of credit valuation adjustment (CVA) and potential future exposure (PFE). In particular, we present a valuation framework for Bermudan swaptions. The essential idea is to approximate the required value function via a set of risk-neutral scenarios and use this approximated value function on the set of observed real-world scenarios. This technique significantly improves the computational efficiency by avoiding nested Monte Carlo simulation and using only basic methods such as regression. We demonstrate the benefits

Accelerating XVA Calibration Using Multi-level Monte Carlo

“…Note that due (4) for all λ ∈ [a, b]. The estimator [3] for CVA(A, λ) is then given as TECHNICAL PAPER coarse estimation on the refined grids G i , i = 1, … , L with higher computational costs but with a lower number of path simulations. Depending on the variances of the corrections, we can achieve strong efficiency gains with this method.…”

“…Finally, in all numerical examples, we choose the time grid for the estimators [3] and [5] as follows: we use monthly time steps in the simulation up to 1 year and quarterly steps after the first year and we simulate 10 years, which gives M = 48.…”

“…The focus in this article will be on CVA on portfolios of plain vanilla derivatives only, but the method presented herein is applicable for exotic derivatives as well. Efficient Monte Carlo techniques for CVA on exotic derivatives, such as Bermudan swaptions, are addressed in Antonov et al (2011), Feng et al (2016), and Karlsson et al (2016).…”

Computing Credit Valuation Adjustment for Bermudan Options With Wrong Way Risk

“…The former is based on Fourier transformation, and the latter is a combination of regression, path bundling and Monte Carlo simulation. Employing these two approaches for efficient computation of exposure profile on both real-world and risk-neutral scenarios, without sub-simulation, can be found in Feng et al (2016).…”

Neural Network for Pricing and Universal Static Hedging of Contingent Claims

“…Pelsser and Schweizer [2016] show that as the approximation error from the regression in the regress later approach vanishes, the coefficients obtained are perfect regardless of the measure used for calibration. This property can be leveraged for problems where one has to work with mixed probability measures, examples of which include computing potential future exposures of Bermundan Swaptions in Feng et al [2016], and computing the capital valuation adjustment in Jain et al [2019a], where one has to work simultaneously with both the risk-neutral and the real-world measures. A common problem faced by both, the regress now and the regress later approaches -when a linear model is used for the regression-is that the selection of the basis functions for the regression is arbitrary and varies between different payoffs.…”