Convexity adjustments \`a la Malliavin
David Garc\'ia-Lorite, Raul Merino
TL;DR
This paper introduces a Malliavin calculus-based method to approximate convexity adjustments for interest rate derivatives, demonstrating high numerical accuracy across various products within a one-factor Cheyette model.
Contribution
It presents a novel Malliavin calculus approach to derive convexity adjustments for multiple interest rate products, offering a simple and accurate approximation method.
Findings
Accurate convexity adjustment formulas for Futures, OIS Futures, FRAs, and CMSs.
High numerical precision demonstrated in the Cheyette model.
Method simplifies the calculation process for interest rate derivatives.
Abstract
In this paper, we develop a novel method based on Malliavin calculus to find an approximation for the convexity adjustment for various classical interest rate products. Malliavin calculus provides a simple way to get a template for the convexity adjustment. We find the approximation for Futures, OIS Futures, FRAs, and CMSs under a general family of the one-factor Cheyette model. We have also seen the excellent quality of the numerical accuracy of the formulas obtained.
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Taxonomy
TopicsStochastic processes and financial applications · Economic theories and models · Monetary Policy and Economic Impact