Interest Rate Swaps and Their Derivatives: A Practitioner's Guide

CHAPTER 7

European-Style Interest-Rate Derivatives

Recall that the correct price (coming from a self-financing replicating portfolio) for European-style interest rate options is the risk-neutral expectation of the stochastically discounted option payoff:

where in a risk-neutral world, prices of underlying assets (zero-coupon bonds) must satisfy

While the preceding is the right framework for pricing interest rate options, market practice is to try to use Black′s Formula as much as possible, resorting to the above framework only when it cannot be co-opted in any reasonable shape or form!

The common misapplication is to approximate

and to further assume that rates are tradeable assets, and evaluate E₀[C(t_e, ω)] by using Black′s Formula with forward rates rather than forward asset values. Chapter 11 shows how using Black′s formula as used in practice can be justified using the forward measure lens, but for this chapter, we will simply illustrate the market practice for common products.

MARKET PRACTICE

Market practice is to use Black′s Formulae for pricing and hedging flow products despite the theoretical inconsistency of treating discounting as deterministic, while interest rates ...