Basket CMS Derivatives in Term Structure Market Models with Stochastic Volatility

Abstract

We consider the pricing of Caps and Floors on CMS baskets in term structure models. To this end we shortly review CMS indices and the market for financial products based on these indices.

Having specified the financial products we review two popular Stochastic Volatility Libor Market Model frameworks for pricing interest rate derivatives and show how to derive (semi-) analytical pricing formulas within these frameworks. The stochastic volatility is of Heston or SABR type.

Our proposed methods do not only allow the fast pricing of basket CMS Caps and Floors but they can also be applied to calibrate the market models by taking into account market quotes for CMS and CMS spread options.

Keywords: Libor Market Model, Stochastic Volatility, CMS, Markovian Projection, Parameter Averaging, Spread Options