In Search of ″The″ Model
The rates markets have experienced explosive growth over the last 25 years, starting with the first interest-rate swaps in the 1980s to the introduction of swaptions in mid-1980s and structured note programs in the early 1990s. While in the early days, swaps were thought and explained via comparative advantage theories, these were soon replaced by the current arbitrage-free arguments relating them to discount and forward curves. As such, other than the date-related minutiae and shifting of focus from prices to rates, the pricing of swaps are not that different from bonds. For simple interest-rate derivatives, many option pricing formulae and concepts were borrowed from equities and co-opted to interest rates. However, callable bonds and the evolving structured note programs in the early 1990s necessitated a more thorough approach, leading to various term structure models based on either the short-rate or the full-term structure.
MIGRATION TO FULL-TERM STRUCTURE MODELS
In the early days, with the large margins associated with newfangled products, it was sufficient to have some model—however rudimentary—that could price complex payoffs. Most firms in the early 1990s started with a short-rate model, either BDT/BK with multifactor extensions, or a Hull-White model. These models were adequate for pricing simple interest-rate products and Bermudans in the tree implementation, and path-dependent options in simulation implementation, although ...