A the need to consider interest rate uncertainty in their decisions. This increased awareness results in a growing demand for financial mechanisms capable of transferring risk between parties in a transaction. For many years interest rate futures contracts were the only method available to accomplish such goals. Over the last decade, however, a number of new instruments, such as exchange traded debt options and over-the-counter products such as forward rate agreements, swaps, caps and floors have been introduced. The phenomenal growth of the over-the-counter market is evidenced by the fact that the notional principal underlying the swap, cap and floor market is rapidly approaching one trillion dollars.
In most cases over-the-counter products are tailor-designed risk management products that consist of a host of contingent claims whose payouts are based on interest rates drawn from a variety of points across the yield curve. To value these complex claims it is often necessary to decompose them into a portfolio of simple put and call options. Fundamental then, to any valuation model for complex interest rate claims, is a simple model for valuing simple put and call options along the yield curve. Central to this issue is the incorporation of uncertainty into term structure models in a satisfactory way. There are currently three different approaches used to incorporate uncertainty into the yield curve process and to value interest rate claims.
This article reviews these approaches and identifies the approach that is most useful for pricing portfolios of claims whose values are contingent on interest rates drawn from different points along the yield curve. This approach, referred to as the term structure constrained approach (TSC) is then expanded upon. Examples are provided to illustrate the methodology. The first example investigates the pricing of interest rate futures and forwards. The futures price of a claim that contains an embedded quality option is also valued. Finally, more complex claims are analyzed and This work was done while the first author was visiting the University of Southern California.