December 2015
Intermediate to advanced
368 pages
8h 7m
English
Content preview from Finance, Economics, and Mathematics
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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Unpublished memorandum, 1979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
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
Integrate Eq. (3) over u from t to 
. We get
4 
Now differentiate ...
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