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Convexity adjustment for constant maturity swaps in a multi-curve framework

Nikolaos Karouzakis (), John Hatgioannides () and Kostas Andriosopoulos ()
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Nikolaos Karouzakis: University of Sussex
John Hatgioannides: City University London
Kostas Andriosopoulos: ESCP Europe Business School

Annals of Operations Research, 2018, vol. 266, issue 1, 159-181

Abstract: Abstract In this paper we propose a double curving setup with distinct forward and discount curves to price constant maturity swaps (CMS). Using separate curves for discounting and forwarding, we develop a new convexity adjustment, by departing from the restrictive assumption of a flat term structure, and expand our setting to incorporate the more realistic and even challenging case of term structure tilts. We calibrate CMS spreads to market data and numerically compare our adjustments against the Black and SABR (stochastic alpha beta rho) CMS adjustments widely used in the market. Our analysis suggests that the proposed convexity adjustment is significantly larger compared to the Black and SABR adjustments and offers a consistent and robust valuation of CMS spreads across different market conditions.

Keywords: Convexity adjustment; Constant maturity swaps; Multi-curve framework; Yield curve modelling; Money market instruments (search for similar items in EconPapers)
Date: 2018
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