Levy-Swaption 가치 평가 모형

The Swaption is one of the popular interest rates derivatives. In spite of such a popularity, the swaption pricing formula is hard to derived within the theoretical consistency. Most of swaption pricing model are heavily depending on the simulation technique. We present a new class of swaption model based on the multi-factor HJM Levy-mixture model. A key contribution of this paper is to provide a generalized swaption pricing formula encompassing many market stylize facts. We provide an approximated closed form solution of the swaption price using the Gram-Charlier expansion. Specifically, the solution form is similar to the market models, since our approximation is based on the Lognormal distribution. It can be directly compared with the traditional Black’s formula when the size of third and fourth moments are not so large. The proposed extended Levy model is also expected to be capable of producing the volatility smiles and skewness.