The Pricing of Interest Rate Contingent Claims

Abstract

The most important result in this working paper is the construction of a multidimensional Gaussian interest-rate term structure model, where, based on a construction of equivalent martingale measures and a suitable selection of numerators, it is shown that it is possible to derive analytical expressions for a wide range of derived instruments.The instruments for which analytical expressions are derived in this connection are forward contracts, futures contracts, options on zero-coupon bonds, options on interest rates (including options on the slope and curvature of the term structure of interest rates), caps and floors, options on both forward contracts and futures contracts, options on CIBOR futures, including options on FRAs, the pricing of floating-rate bonds, swaps, swaptions and, finally, options on coupon bonds.As regards the price expression for options on coupon bonds, a generalization is made of the Karoui, Myneni and Viswanathan (1993) model. The analytical expression derived here is namely a real analytical expression as opposed to Karoui, Myneni and Viswanathan which must be considered to be a semi-analytical expression.Using numerical tests we even managed to show that this new “true” closed form formula for the pricing of options on coupon bonds even seems to be valid in a general multi-factor Markovian HJM framework.