Options in and on interest rate futures contracts: results from martingale pricing theory

In this paper we address the theoretical problem of evaluating the quality option embedded in interest rate futures contracts. We use the martingale properties of the prices of interest-rate contingent claims under different probability measures in order to derive solutions for the value of futures and options on futures, accounting for the quality option and assuming a square-root model for the short rate. The futures pricing formula boils down to a simple linear combination of the futures prices of the zero-coupon bonds which constitute the deliverable bonds. A European call option on such a futures can be rewritten as an option on a single futures in which the strike price is 'curved', i.e. it is a decreasing function of the short rate.