9.3 Matching the lognormal distribution


9.3 Matching the lognormal distribution

We have assumed the short-term interest rate has a lognormal distribution at any time horizon. This means we require only a mean and standard deviation to fully specify its distribution. However, in the BK model, three factors are required to describe the short-term interest rate process - the target rate, mean reversion speed and local volatility. This means that for a given time horizon, the solution is not unique and the distribution of short- term interest rates may be matched by a family of possible processes.

These processes will differ in their mean reversion and local volatility characteristics. Strong mean reversion means a move away from the target rate is quickly reversed , which is not the case for weaker mean reversion. Hence, a narrow (wide) distribution of the short-term interest rate in the future may result from either strong (weak) mean reversion or low (high) local volatility.




Interest Rate Modelling
Interest Rate Modelling (Finance and Capital Markets Series)
ISBN: 1403934703
EAN: 2147483647
Year: 2004
Pages: 132
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