Notes and Comments: An approximation of caplet implied volatilities in Gaussian models

It is market practice to quote interest rate derivatives traded "over the counter" in terms of their implied volatility. For this reason, the term structure of at-the-money cap volatilities as well as the volatility surface of at-the-money swaptions are directly observed. This paper analyz...

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Bibliographic Details
Published in:Decisions in economics and finance 2006-02, Vol.28 (2), p.113-127
Main Authors: Angelini, Flavio, Herzel, Stefano
Format: Article
Language:English
Subjects:
Approximation
Brownian motion
Capital markets
Economic models
Interest rates
Random variables
Standard deviation
Studies
Volatility
Zero coupon bonds
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Summary:It is market practice to quote interest rate derivatives traded "over the counter" in terms of their implied volatility. For this reason, the term structure of at-the-money cap volatilities as well as the volatility surface of at-the-money swaptions are directly observed. This paper analyzes the case of caps. Any analysis of these markets would most likely report two main facts. The first is that the level of the volatility is inversely related to the level of the interest rates. The second is that the term structure is either a decreasing or a humped function of maturity. For a reference, see Rebonato (2003) and Brigo and Mercurio (2001). Rebonato (2003) suggests that the structure of implied volatility is humped in periods of normal market conditions and decreasing when markets are "excited". Interpreting and explaining such phenomena is indeed an interesting and important issue. [PUBLICATION ABSTRACT]
ISSN:1593-8883
1129-6569
DOI:10.1007/s10203-005-0056-7