Extracting Probabilistic Information from the Prices of Interest Rate Options: Tests of Distributional Assumptions

It has been observed that return distributions in general and interest rates in particular exhibit skewness and kurtosis that cannot be explained by the lognormal distribution commonly used as an assumption in many option pricing models. We have replaced the lognormal assumption in the Black (1976) model with the g-and-h distribution and derived a simple, closed-form option pricing formula under the no-arbitrage framework for pricing European options. We measured its performance using interest rate cap data and compared it with the option prices based on the Lognormal, Burr-3, Weibull, and GB2 distributions. We observed that the g-and-h distribution exhibited a high degree of accuracy in pricing options and was found to be much better than these other distributions in extracting probabilistic information from the option market.