A multinomial tree model for pricing credit default swap options
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Abstract
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 Tucker and Wei (J Fixed Income 15(1):88–95, 2005). 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.
Keywords
Credit default swap Option Multinomial tree Moment matchingPreview
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References
- AitShalia F, Lai TL (2001) Exercise boundaries and efficient approximations to American option prices and hedge parameters. J Comput Fin 4(4): 85–103Google Scholar
- Basso A, Nardon M, Pianca P (2004) The two-step simulation procedure to analyze the exercise features of American options. Decis Econ Fin 27(1): 35–56MATHCrossRefMathSciNetGoogle Scholar
- Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81(3): 637–659CrossRefGoogle Scholar
- Black F (1976) The pricing of commodity contracts. J Fin Econ 3(1/2): 167–179CrossRefMathSciNetGoogle Scholar
- Cox JC, Ingersoll JE, Ross SA (1985) A theory of the term structure of interest rates. Econometrica 53(2): 385–406CrossRefMathSciNetGoogle Scholar
- Cox JC, Ross SA, Rubinstein M (1979) Option pricing: a simplified approach. J Fin Econ 7(3): 229–263MATHCrossRefGoogle Scholar
- Glasserman P, Zhao X (2000) Arbitrage-free discretization of lognormal forward Libor and swap rate models. Fin Stoch 4(1): 35–68MATHCrossRefMathSciNetGoogle Scholar
- Hull J (2006) Options, futures, and other derivatives. Prentice Hall, New YorkGoogle Scholar
- Jabbour G, Kramin M, Kramin T, Young S (2005) Multinomial lattices and derivatives pricing. In: Lee CF (ed) Advances in quantitative analysis of finance and accounting, vol. 2(5). World Scientific, Singapore, pp 1–15CrossRefGoogle Scholar
- Jarrow R, Rudd A (1983) Option pricing. Irwin, HomewoodGoogle Scholar
- Ju N (1998) Pricing an American option by approximating its early exercise boundary as a multipiece exponential function. Rev Fin Studies 11(3): 627–646CrossRefGoogle Scholar
- Ki H, Choi B, Chang KH, Lee M (2005) Option pricing under extended normal distribution. J Futures Mark 25(9): 845–871CrossRefGoogle Scholar
- Kim IJ, Byun SJ (1994) Optimal exercise boundary in a binomial option pricing model. J Fin Eng 3(2): 137–158Google Scholar
- Kwok YK (2008) Mathematical models of financial derivatives. Springer, New YorkMATHGoogle Scholar
- Little T, Pant V, Hou C (2000) A new integral representation of the early exercise boundary for American put options. J Comput Fin 3(3): 73–96Google Scholar
- Longstaff F, Stanta-Clara P, Schwartz E (2001) The relative valuation of caps and swaptions: theory and empirical evidence. J Fin 56(6): 2067–2109CrossRefGoogle Scholar
- Nelson DB, Ramaswamy K (1990) Simple binomial process as diffusion approximations in financial models. Rev Fin Studies 3(3): 393–430CrossRefGoogle Scholar
- Tucker A, Wei J (2005) Credit default swaptions. J Fixed Income 15(1): 88–95CrossRefGoogle Scholar
- Vasicek O (1977) An equilibrium characterization of the term structure. J Fin Econ 5(2): 177–188CrossRefGoogle Scholar