Valuation of CMS Spread Options with Nonzero Strike
Rates in the LIBOR Market Model

Abstract

The LIBOR market model has become the industry standard for modeling interest-dependent options, such as caps. The forward rate for every maturity is lognormal, so the cap is decomposed into individual caplets, each of which can be priced simply with the Black model. A swap rate, however, averages forward interest rates at multiple future dates, so as the weighted sum of lognormal variables, it is not lognormal. Nor is the spread between two lognormal interest rates, such as that between constant maturity swap (CMS) rates for different maturities. As a result, popular kinds of contracts, such as CMS spread options, are typically priced using computationally intensive Monte Carlo simulation. Wu and Chen propose approximating the actual density with a generalized lognormal, leading to a closed-form valuation model that is accurate and much faster to implement than simulation.