Credit Spread Specification and the Pricing of Spread Options

This paper presents a simple approach to the pricing of options on spread and some arguments in favor of modelling the spread using its two components instead of the spread itself. We show that, even in a simple Gaussian setting, the spread should not be modelled directly, and that convergence speeds of the two components are crucial parameters. There exist conditions, discussed in this paper, under which the analysis can be reduced to a two-factor model based on the dynamics of the spread itself. Hence, we propose a three-factor model based on the dynamics of the riskless rate and of the two components of the spread. This is done by following the Longstaff (1990) methodology and with the assumption that both the riskless rate and the spread or its two components follow correlated Ornstein-Uhlenbeck processes. Greeks analysis shows that spread options have some very specific features compared to the Black-Scholes-Merton (1973) option model. Moreover, the results show that the mispricing is important and not systematic when one chooses a spread option model based on the dynamics of the spread instead of using the dynamics of its two components. We finally show how the spread option model allows us to price other yield derivatives, like options to exchange a yield for another or the options on the maximum or the minimum of two yields.