Finance, Economics, and Mathematics

Chapter 7The Liquidity Premium

Unpublished memorandum, 1979

Let the price at time u of a discount bond maturing at time v be described by the stochastic differential equation

1

where is a Wiener process. As shown in Vasicek (1977) (Chapter 6 of this volume), the mean and volatility σ(u, v) of the instantaneous rate of return are related by

2

where is the spot rate and is the market price of risk. Eq. (1) can be written as

3

Integrate Eq. (3) over u from t to . We get

4

Now differentiate ...