TABLE OF CONTENTS Before we start exploring specific models for pricing credit derivatives, we will pause to introduce some notation and, in the process, review a few important concepts. Those familiar with risk-neutral probabilities and the risk-neutral valuation approach, two of the most important topics discussed in this chapter, may still want to at least glance through the next few pages to familiarize themselves with the notation that will be used throughout this part of the book.
In this chapter we shall assume that riskless interest rates are deterministic. This is done for expositional purposes only so we can avoid certain technical details related to the discussion of the risk-neutral valuation in Section 15.2. [1] Stochastic interest rates are discussed in Chapter 17.
Let Z( t, T) denote today s (time- t) price of a riskless zero-coupon bond that pays out $1 at a future time T. If R( t, T) is the continuously compounded yield to maturity on this bond, we have [2]
| (15.1) |  |
We can think of Z( t, T) as reflecting the time-value of money, or today s (time- t) value of $1 that will be received for sure at time T. Note that, for positive interest rates, even though the terminal payout of this bond is never in question, its value today...
