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

36 Pages Posted: 10 Apr 2009 Last revised: 25 Feb 2017

See all articles by Wolfram Boenkost

Wolfram Boenkost

Lucht Probst Associates GmbH

Wolfgang M. Schmidt

Frankfurt School of Finance & Management

Date Written: June 27, 2016

Abstract

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

Boenkost, Wolfram and Schmidt, Wolfgang M., Notes on Convexity and Quanto Adjustments for Interest Rates and Related Options (June 27, 2016). Available at SSRN: https://ssrn.com/abstract=1375570 or http://dx.doi.org/10.2139/ssrn.1375570

Wolfram Boenkost

Lucht Probst Associates GmbH ( email )

Grosse Gallusstr. 9
Frankfurt, 60311
Germany

HOME PAGE: http://www.l-p-a.com

Wolfgang M. Schmidt (Contact Author)

Frankfurt School of Finance & Management ( email )

Adickesallee 32-34
Frankfurt am Main, 60322
Germany

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