Caps and Swaptions are basic LIBOR interest rate options. In order to conveniently generate strings of cap and swaption prices, practitioners use Markov models of interest rates. There are not many of these. Ritchen and Sanakar. introduced a well known class, generalized Vasicek models. A broader class is due to Rogers. I describe two undesirable features of pricing with these models and then offer a fix.
Statistical analyses of forward interest rate behavior suggest volatility choices that can not be incorporated in these models. I describe the choices and explain how to set up computationally powerful, arbitrage-free models with them. The prototype is the forbidden model of term structure.
One may condition the forbidden model to make it both attractive and computationally useful. Basic calculations produce explicit formulas for caplet and swaption prices. In this model, caplet prices agree numerically with the industry-standard Black formula. I discuss the assumption made by the industry that swap rates have log normal behavior under forward measures and present an alternative swaption price formula. In the talk I mention several open problems some computational, some theoretical that are connected with these new models of term structure.
Speaker: Victor Goodman, Indiana University
Slides: (TBA)