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Conversion method of cap vols across tenors
The case of the 12M Euribor index
This article describes a simple procedure for approximating the cap volatility corresponding to the 12M Euribor tenor. We compare the resulting expression in the single- and dual-curve worlds.
Underlying liabilities can often be linked to floating mortgages or other floating loans, the rate of which is adjusted annually. Risk managers and traders that wish to value or hedge such liabilities are in principle required to value a position on a 12M underlying index rate. Unfortunately there is no liquid quoted data for such an index on most of the data providers, including Bloomberg. This brings in a necessity to invent a methodology for the construction of an arbitrage-free way to extrapolate the 12M cap vols from another tenor.
In this article we describe a simple conversion method that takes as input the 6M EUR cap vols and outputs the 12M cap vols. The method is exact under the single-curve assumption. We provide some justification for its validity under the dual-curve assumption. Finally, some comparisons are given versus Bloomberg’s Swap Manager.
Although the presented case study refers to the EURIBOR 12M, the methodology can be easily translated to other currencies and underlyings.