The volatility term structure in a lognormal process for the short rate

Georges Darbellay

The European Journal of Finance, 2003, vol. 9, issue 1, 92-103

Abstract: One-factor Markov models are widely used by practitioners for pricing financial options. Their simplicity facilitates their calibration to the intial conditions and permits fast computer Implementations. Nevertheless, the danger remains that such models behave unrealistically, if the calibration of the volatility is not properly done. Here, we study a lognormal process and investigate how to specify the volatility constraints in such a way that the term structure of volatility at future times, as implied by the short rate process, has a realistic and stable shape. However, the drifting down of the volatility term structure is unavoidable. As a result, there is a tendency to underestimate option prices.

Date: 2003
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DOI: 10.1080/13518470010011233

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