Encyclopedia of Quantitative Finance, IV Volume Set

Nested Monte Carlo see Nested Simulation

Nested Simulation

Stochastic default-intensity (“reduced-form”) models are widely applied in the pricing of single-name credit instruments such as credit default swap (CDS) and corporate bonds (see Duffie–Singleton Model; Intensity-based Credit Risk Models). Duffie and Gârleanu [5]demonstrate how collateralized debt obligations (CDO) tranches may be priced using a multiname extension of the stochastic intensity framework (see Multiname Reduced Form Models). This article remains influential as a conceptual benchmark, but practitioners generally find the computational burden of this model prohibitive for real-time trading.^a

Risk-management applications introduce additional challenges. Time constraints are less pressing than in trading applications, but the computational task may appear more formidable. When loss is measured on a mark-to-market basis, estimation via simulation of VaR and other risk measures calls for a nested procedure: In the outer step, one draws realizations of all default intensities up to the horizon, and in the inner step one uses simulation to reprice each instrument in the portfolio at the horizon conditional on the realized intensities. At first glance, simulation-based pricing algorithms would seem to be impractical in the inner step, because the inner pricing simulation must be executed for each trial in the outer ...