9. November 2007

Notes on Convexity and Quanto Adjustments for Interest Rates and Related Options

We collect simple and pragmatic exact formulae for the convexity adjustment

of irregular interest rate cash flows as Libor-in-arrears or payments of

a swap rate (CMS rate) at an irregular date. The results are compared with

the results of an approximative approach available in the popular literature.

For options on Libor-in-arrears or CMS rates like caps or binaries we derive

an additional new convexity adjustment for the volatility to be used in a

standard Black & Scholes model.

Key words: interest rate options, convexity, quanto adjustment, change of


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