Notes on Convexity and Quanto Adjustments for Interest Rates and Related Options
36 Pages Posted: 10 Apr 2009 Last revised: 25 Feb 2017
Date Written: June 27, 2016
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 and Bachelier model. We study the quality of the adjustments comparing the results of the approximative Black & Scholes formula with the results of an exact valuation formula. Further we investigate options to exchange interest rates which are possibly set at different dates or admit different tenors.
We collect general quanto adjustments formulae for variable interest rates to be paid in foreign currency and derive valuation formulae for standard options on interest rates paid in foreign currency.
First version October 2003. Last updated in June 2016 to incorporate the Bachelier model for negative interest rates.
Keywords: interest rate options, convexity, quanto adjustment, change
JEL Classification: G13
Suggested Citation: Suggested Citation