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A note on the volatility term structure in short rate models
Author(s) -
Darbellay Georges A.
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19980781516
Subject(s) - volatility (finance) , stochastic volatility , short rate , sabr volatility model , econometrics , forward volatility , volatility smile , implied volatility , economics , volatility swap , log normal distribution , local volatility , variance swap , yield curve , mathematics , interest rate , statistics , finance
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”.