In this article, we develop a technique of parameter averaging and Markovian projection on a quadratic volatility model based on a term-by-term matching of the asymptotic expansions of option prices in volatilities. In doing so, we revisit the procedure of asymptotic expansion and show that the use of the product formula for iterated Itô integrals leads to a considerable simplification in comparison with the approach currently prevalent in the literature. Results are applied to the classic problem of LIBOR Market Model (LMM) swaption pricing. We confrm numerically that the retention of the quadratic term gives a marked improvement over the standard approximation based on the projection on a displaced diffusion.

Authors: A. Antonov and T. Misirpashaev

Download Numerix Research Paper

Complete the form below to download this complimentary research paper.

Select Form: 

Form #5: Research

Keep me informed of future research from Numerix:

Sign me up to receive "Derivative Insights & Innovations" monthly newsletter by Numerix:

* Required fields
newsletter issue - Nov 9, 2017

Derivative Insights & Innovations - November 2017 Issue

newsletter issue - Oct 12, 2017

Derivative Insights & Innovations - October 2017 Issue

newsletter issue - Sep 14, 2017

Derivative Insights & Innovations - September 2017 Issue

newsletter issue - Feb 9, 2017

Derivative Insights & Innovations - February 2017 Issue

newsletter issue - Jan 12, 2017

Derivative Insights & Innovations - January 2017 Issue

journal issue

Numerix Journal Vol. 3, No. 2

newsletter issue - Dec 8, 2016

Derivative Insights & Innovations - December 2016 Issue

newsletter issue - Nov 10, 2016

Derivative Insights & Innovations - November 2016 Issue

newsletter issue - Sep 22, 2016

Derivative Insights & Innovations - September/October 2016 Issue

video blog

AAD, GPU, FRTB and the Demands of Technology

journal issue

Numerix Journal Vol. 3, No. 1

newsletter issue - Aug 4, 2016

Derivative Insights & Innovations - August 2016 Issue