A note on the volatility term structure in short rate models

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 78; no. S3; pp. 885 - 886
• Main Author: Darbellay, Georges A.
• Format: Journal Article
• Language: English
• Published: Berlin Wiley-VCH Verlag 1998; Wiley‐VCH Verlag
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.19980781516

In finance, interest rate option models based on a stochastic process for the short rate are widely used by practitioners, yet the calibration of their volatility input is not as straightforward as it seems. One problem with these Markovian one‐factor models is that they cannot reproduce an arbitrary volatility curve. They can be made to fit any initial volatility function but the volatility curve being assumed at future times is liable to be quite different from that being assumed initially. 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, remains “stable”.