Prentice Hall - Options, Futures, and Other Derivative Securities - John C,. Hull - 5th, 2002

OCR版本，可复制粘贴，全书756页，文件格式PDF，大小不到6M，分为4个RAR压缩文件，再也不用看清华那个阉割版本了。

下面是随便从书中选取一页复制的样品。

C H A P T E R 23

INTEREST RATE DERIVATIVES:
MODELS OF THE SHORT RATE
The models for pricing interest rate options presented in Chapter 22 make the assumption that the
probability distribution of an interest rate, a bond price, or some other variable at a future point in
time is lognormal. They are widely used for valuing instruments such as caps, European bond
options, and European swap options. However, they have limitations. They do not provide a
description of how interest rates change through time. Consequently, they cannot be used for
valuing interest rate derivatives such as American-style swap options, callable bonds, and
structured notes.
This chapter and the next discuss alternative approaches for overcoming these limitations. These
involve building what is known as a term structure model. This is a model describing the evolution
of the zero curve through time. In this chapter we focus on term structure models that are
constructed by specifying the behavior of the short-term interest rate, r.

23.1 EQUILIBRIUM MODELS
Equilibrium models usually start with assumptions about economic variables and derive a process
for the short rate, r. They then explore what the process for r implies about bond prices and option
prices. The short rate, r, at time t is the rate that applies to an infinitesimally short period of time at
time t. It is sometimes referred to as the instantaneous short rate. It is not the process for r in the real
world that matters. Bond prices, option prices, and other derivative prices depend only on the
process followed by r in a risk-neutral world. The risk-neutral world we consider here will be the
traditional risk-neutral world, where, in a very short time period between t and t + St, investors earn
on average r(t) St. All processes for r that we present will be processes in this risk-neutral world.
From equation (21.19), the value at time t of an interest rate derivative that provides a payoff of
fT at time T is