Exact scenario simulation for selected multi-dimensional stochastic processes

Platen, Eckhard; Rendek, Renata

doi:10.31390/cosa.3.3.09

Cited by 5 publications

(2 citation statements)

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“…By using an exact simulation scheme, we can eliminate these problems. In Appendix D, we propose the exact simulation of two correlated squared Bessel processes as explained in Platen and Rendek (2009). Recall that the discounted GOPS δ * t is a time transformed squared Bessel process of dimension four with some deterministic transformed time.…”

Section: Monte Carlo Simulationsmentioning

confidence: 99%

“…More specifically, by assuming independence between the discounted GOP and the default-adjusted short rate, we first obtain closed form expressions for the prices of defaultable bonds and potentially other derivatives. Then in the more general case, we use an exact simulation scheme, in the spirit of Platen and Rendek (2009), which guarantees strict positive paths. However, like with any raw Monte-Carlo simulations, it can become computationally expensive and therefore, a variance reduction technique is highly recommended.…”

Section: Introductionmentioning

confidence: 99%

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Alternative Defaultable Term Structure Models

et al. 2009

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The objective of this paper is to consider defaultable term structure models in a general setting beyond standard riskneutral models. Using as numeraire the growth optimal portfolio, defaultable interest rate derivatives are priced under the real-world probability measure. Therefore, the existence of an equivalent risk-neutral probability measure is not required. In particular, the real-world dynamics of the instantaneous defaultable forward rates under a jump-diffusion extension of a HJM type framework are derived. Thus, by establishing a modelling framework fully under the real-world probability measure, the challenge of reconciling real-world and risk-neutral probabilities of default is deliberately avoided, which provides significant extra modelling freedom. In addition, for certain volatility specifications, finite dimensional Markovian defaultable term structure models are derived. The paper also demonstrates an alternative defaultable term structure model. It provides tractable expressions for the prices of defaultable derivatives under the assumption of independence between the discounted growth optimal portfolio and the default-adjusted short rate. These expressions are then used in a more general model as control variates for Monte Carlo simulations of credit derivatives.

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Section: Monte Carlo Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%