Interest Rate Modelling (Finance and Capital Markets Series)

8.6 Conclusion

The BDT model has several positive features:

• for positive value of the decay factor (reversion speed) the general shape of the term structure of volatilities which is captured within the BDT model is consistent with the market- observed volatility term structure.

• due to the lognormal process assumed for the short-term interest rate, calibration to market prices becomes much simpler. It is possible to fit the model to both the yield curve and to cap volatilities at the same time. Hence the model can simultaneously reproduce the prices of various maturity caps, displaying a declining term structure of volatilities.

However, it also displays several problems:

• as with all one factor interest rate models the changes in rates of various maturities are by and large parallel which is not consistent with market observation. Hence the BDT model is not able to capture a tilting effect on the yield curve. This would require a second factor.

• no specification is made of the evolution, through time, of the term structure of volatilities.

• since the future short-term interest rate volatilities fully determine the term structure of volatility it is impossible to specify one independently of the other.

This model was developed by practitioners for practitioners and hence allows for easy calibration to observed data and easy pricing of European and American style contingent claims.