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A multinomial tree model for pricing credit default swap options. (English) Zbl 1304.65022

Summary: Among the traded credit derivatives, the market interest in credit default swap options (CDSwaptions) is enormous. We propose a multinomial tree model to price Bermudan CDSwaptions. Our basic rationale is that we distribute the occurring probability for each node in a branch proportional to the probability density function of the assumed (normal) distribution. Through this approach, without the need of solving a large number of equations simultaneously, only the first four moments are required to build an arbitrarily large \(N\)-branches tree. We also demonstrate the detailed model implementation procedure including the valuation and the estimation of critical prices through an empirical example in [A. L. Tucker and J. Z. Wei, “Credit default swaptions“, J. Fixed Income 15, No. 1, 88–95 (2005; doi:10.3905/jfi.2005.523092)]. Numerical results show that, in the valuation, the proposed multinomial tree model is accurate and can significantly save pricing time under the same degree of accuracy as the binomial tree model. In the estimation of critical prices, the results are less accurate than those in the valuation, but the relative errors are acceptable.

MSC:

62-08 Computational methods for problems pertaining to statistics
91G20 Derivative securities (option pricing, hedging, etc.)
91G40 Credit risk
91G60 Numerical methods (including Monte Carlo methods)
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