Modelling, Pricing, and Hedging Counterparty Credit Exposure

AAD and least-square Monte Carlo: Fast Bermudan-style options and XVA Greeks

“…However, only for vanilla securities and simple models for the evolution of the risk factors, such conditional future exposures can be expressed in closed form, and regression based Monte Carlo is commonly employed to produce approximate estimators see, e.g., Cesari et al (2009).…”

“…In this paper we present the application of AAD to regression-based MC approaches (also known as least-square MC) such as those that are widely utilised for Bermudan-style options, see Carriere (1996); Tsitsiklis and Van Roy (2001); Longstaff and Schwartz (2001), or for XVA applications, see Cesari et al (2009) and Joshi and Kwon (2016). We develop the AAD implementation of the well-known least-square algorithm for the computation of conditional expectations, and we investigate numerically the impact on the Greeks arising from the sensitivities of the regression functions, a component that is generally ignored for Bermudan-style options by invoking arguments of quasi-optimality of the exercise boundary.…”

Toward a coherent Monte Carlo simulation of CVA

“…Using the same argument presented in (10) and (11), the dependence according to τ is not an important issue for computations performed in Section 3. In fact, the conditional expectation (7) is equal to…”

“…In a financial transaction between a party A that has to pay another party B some amount V , the CVA value is the price of the insurance contract that covers the default of party A to pay the whole sum V . In other words, in the absence of arbitrage opportunities, the CVA is the value of liquid products that must be saved to deal with counterparty default (see [9,10]). …”

“…We will see that MCM is justified by its computational complexity which is smaller than square Monte Carlo, in particular for the CVA that involves American contracts. Moreover, in contrast to regression methods used in [10], we will justify that MCM is a nonparametric method whose accuracy depends only on the number of simulated trajectories. Consequently, one can increase "indefinitely" the accuracy by simulating more trajectories and using more computational resources thanks to an efficient parallel implementation.…”