17 - Interest Rate Derivatives
from Part Four - Interest Rate Derivative Products
Published online by Cambridge University Press: 05 June 2012
Summary
Introduction
One of the biggest assumptions we have so far made in this book is that interest rates are constant or, at least, known functions of time. In reality this is far from the case. Although the effects of interest rate changes on traded-option prices are relatively small, because of their short lifetime, many other securities that are also influenced by interest rates have much longer duration. Their analysis in the presence of unpredictable interest rates is of crucial practical importance. In the final part of this book, we give a brief introduction to pure interest rate derivative products, and then to products depending on both interest rates and an underlying asset.
We begin in this chapter with the subject of bond pricing. We do this first under the assumption of a deterministic interest rate. This simplification allows us to discuss the effect of coupons on the prices of bonds and the appearance of the yield curve, which we define shortly. Later in the chapter we relax the assumption of deterministic interest rates and present a model which allows the short-term interest rate, the spot rate, to follow a random walk. This leads to a parabolic partial differential equation for the prices of bonds and to models for bond options and many other interest rate derivative products.
Basics of Bond Pricing
A bond is a contract, paid for up-front, that yields a known amount on a known date in the future, the maturity date, t = T.
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- The Mathematics of Financial DerivativesA Student Introduction, pp. 265 - 285Publisher: Cambridge University PressPrint publication year: 1995
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