On pricing of Credit spread options

This paper describes and analyses different pricing models for credit spread options such as Longstaff–Schwartz, Black, Das–Sundaram and Duan (GARCH-based) models. The first two models, Longstaff–Schwartz and Black, assume respectively a mean-reverting dynamic and a lognormal distribution for the spread and are representative of the so-called ‘‘spread models’’. Such models consider the spread as a unique variable and provide closed form solutions for option pricing. On the contrary Das–Sundaram propose a recursive backward induction procedure to price credit spread options on a bivariate tree, which describes the dynamic of the term structure of forward risk-neutral spread and risk-free rate. This model belongs to the class of structural models, which can be used to price a wider range of credit risk derivatives. Finally, we consider the pricing of credit spread options assuming a discrete time GARCH model for the spread.