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Finance, Economics, and Mathematics by Robert C. Merton, Oldrich A. Vasicek

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Chapter 7The Liquidity Premium

Unpublished memorandum, 1979

Let the price c07-math-0001 at time u of a discount bond maturing at time v be described by the stochastic differential equation

1 equation

where c07-math-0003 is a Wiener process. As shown in Vasicek (1977) (Chapter 6 of this volume), the mean c07-math-0004 and volatility σ(u, v) of the instantaneous rate of return are related by

2 equation

where c07-math-0006 is the spot rate and c07-math-0007 is the market price of risk. Eq. (1) can be written as

3 equation

Integrate Eq. (3) over u from t to c07-math-0009. We get

4 equation

Now differentiate ...

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