Fixed Income and Interest Rate Derivative Analysis

CONTINUOUS-TIME FINANCE 155

Now with stochastic interest rates

BT

is random, so the valuation requires

the evaluation of two random quantities expressed as a ratio

CT

and

HT.

But we can change measure to the T-measure by

= EB[p(T, T)/BT]E B

= P(0,

T)ET[CT]

EB[p(T, T) /BT]

In the above we have normalized both B0 and P(T, T) to 1.

11.7

Continuous-time term structure models

Over the past twenty years, research by both academics and finance prac-

titioners has evolved from fairly simple models to more complex ones. A

number of different approaches have been used. At first models ...