Nonlinear Monte Carlo schemes for counterparty risk on credit derivatives. (English) Zbl 1398.91668
Glau, Kathrin (ed.) et al., Innovations in derivatives markets. Fixed income modeling, valuation adjustments, risk management, and regulation. Proceedings of the conference, Munich, Germany, March 30 – April 1, 2015. Cham: Springer Open (ISBN 978-3-319-33445-5/hbk; 978-3-319-33446-2/ebook). Springer Proceedings in Mathematics & Statistics 165, 53-82 (2016).
Summary: Two nonlinear Monte Carlo schemes, namely, the linear Monte Carlo expansion with randomization of M. Fujii and A. Takahashi [Int. J. Theor. Appl. Finance 15, No. 5, Article ID 1250034, 24 p. (2012; Zbl 1262.91159); “Perturbative expansion of FBSDE in an incomplete market with stochastic volatility”, Q. J. Finance 2, No. 3, Article ID 1250015, 24 p. (2012; doi:10.1142/S2010139212500152)] and the marked branching diffusion scheme of P. Henry-Labordère [“Cutting CVA’s complexity”, Risk Mag. 25, No. 7, 67–73 (2012)], are compared in terms of applicability and numerical behavior regarding counterparty risk computations on credit derivatives. This is done in two dynamic copula models of portfolio credit risk: the dynamic Gaussian copula model and the model in which default dependence stems from joint defaults. For such high-dimensional and nonlinear pricing problems, more standard deterministic or simulation/regression schemes are ruled out by Bellman’s “curse of
dimensionality” and only purely forward Monte Carlo schemes can be used.
For the entire collection see [Zbl 1366.91005].
For the entire collection see [Zbl 1366.91005].
MSC:
| 91G60 | Numerical methods (including Monte Carlo methods) |
| 65C05 | Monte Carlo methods |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 91G40 | Credit risk |
| 62P05 | Applications of statistics to actuarial sciences and financial mathematics |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
Citations:
Zbl 1262.91159References:
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