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Convexity Adjustments Made Easy: An Overview of Convexity Adjustment Methodologies in Interest Rate Markets

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  • Nicholas BURGESS

    (University of Reading,)

Abstract

Interest rate instruments are typically priced by creating a non-arbitrage replicating portfolio in a risk-neutral framework. Bespoke instruments with timing, quanto1 and other adjustments often present arbitrage opportunities, particularly in complete markets where the difference can be monetized. To eliminate arbitrage opportunities we are required to adjust bespoke instrument prices appropriately, such adjustments are typically non-linear and described as convexity adjustments. We review convexity adjustments firstly using a linear rate model and then consider a more advanced static replication approach. We outline and derive the analytical formulae for Libor and Swap Rate adjustments in a single and multicurve environment, providing examples and case studies for Libor In-Arrears, CMS Caplet, Floorlet and Swaplet adjustments in particular. In this paper we aim to review convexity adjustments with extensive reference to popular market literature to make what is traditionally an opaque subject more transparent and heuristic.

Suggested Citation

  • Nicholas BURGESS, 2019. "Convexity Adjustments Made Easy: An Overview of Convexity Adjustment Methodologies in Interest Rate Markets," Journal of Economics and Financial Analysis, Tripal Publishing House, vol. 3(2), pages 41-83.
    • Handle: RePEc:trp:01jefa:jefa0032
    DOI: 10.1991/jefa.v3i2.a28
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    References listed on IDEAS

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    1. Nikolaos Karouzakis & John Hatgioannides & Kostas Andriosopoulos, 2018. "Convexity adjustment for constant maturity swaps in a multi-curve framework," Annals of Operations Research, Springer, vol. 266(1), pages 159-181, July.
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    More about this item

    Keywords

    Convexity Adjustments; Radon-Nykodym Derivative; Shifted- Lognormal; Linear Swap Rate Method; Libor In-Arrears Swaps; Constant Maturity Swaps; CMS Caplets; Floorlets and Swaplets.;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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