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Notes on convexity and quanto adjustments for interest rates and related options

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  • Boenkost, Wolfram
  • Schmidt, Wolfgang M.

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 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.

Suggested Citation

  • Boenkost, Wolfram & Schmidt, Wolfgang M., 2003. "Notes on convexity and quanto adjustments for interest rates and related options," Frankfurt School - Working Paper Series 47, Frankfurt School of Finance and Management.
    • Handle: RePEc:zbw:fsfmwp:47
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    References listed on IDEAS

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    15. Heidorn, Thomas & Kantwill, Jens, 2002. "Eine empirische Analyse der Spreadunterschiede von Festsatzanleihen zu Floatern im Euroraum und deren Zusammenhang zum Preis eines Credit Default Swaps," Frankfurt School - Working Paper Series 39, Frankfurt School of Finance and Management.
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    Cited by:

    1. Inklaar, Robert & Koetter, Michael & Noth, Felix, 2012. "Who's afraid of big bad banks? Bank competition, SME, and industry growth," Frankfurt School - Working Paper Series 197, Frankfurt School of Finance and Management.
    2. Dietmar Harhoff & Elisabeth Mueller & John Van Reenen, 2014. "What are the Channels for Technology Sourcing? Panel Data Evidence from German Companies," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 23(1), pages 204-224, March.
    3. Julien Hok & Philip Ngare & Antonis Papapantoleon, 2018. "Expansion formulas for European quanto options in a local volatility FX-LIBOR model," Papers 1801.01205, arXiv.org, revised Apr 2018.
    4. Alexander Libman & Vladimir Kozlov & André Schultz, 2012. "Roving Bandits in Action: Outside Option and Governmental Predation in Autocracies," Kyklos, Wiley Blackwell, vol. 65(4), pages 526-562, November.
    5. Denis Belomestny & Anastasia Kolodko & John Schoenmakers, 2010. "Pricing Cms Spread Options In A Libor Market Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(01), pages 45-62.
    6. Julien Hok & Philip Ngare & Antonis Papapantoleon, 2018. "Expansion Formulas For European Quanto Options In A Local Volatility Fx-Libor Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 1-43, March.
    7. Boeing, Philipp & Mueller, Elisabeth & Sandner, Philipp, 2012. "What makes Chinese firms productive? Learning from indigenous and foreign sources of knowledge," Frankfurt School - Working Paper Series 196, Frankfurt School of Finance and Management.
    8. Yu, Xiaofan, 2011. "A spatial interpretation of the persistency of China's provincial inequality," Frankfurt School - Working Paper Series 171, Frankfurt School of Finance and Management.
    9. Boenkost, Wolfram & Schmidt, Wolfgang M., 2006. "Interest rate convexity and the volatility smile," CPQF Working Paper Series 4, Frankfurt School of Finance and Management, Centre for Practical Quantitative Finance (CPQF).
    10. Böing, Philipp & Müller, Elisabeth, 2012. "Technological Capabilities of Chinese Enterprises: Who is Going to Compete Abroad?," VfS Annual Conference 2012 (Goettingen): New Approaches and Challenges for the Labor Market of the 21st Century 62081, Verein für Socialpolitik / German Economic Association.

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    More about this item

    Keywords

    interest rate options; convexity; quanto adjustment; change of numeraire;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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