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 "Thinking Derivatively" monthly newsletter by Numerix:

* Required fields
conference

Asia Risk Congress Virtual

video blog

Numerix: Pushing Boundaries to Create Breakthrough Technology

product

CrossAsset Structured Finance

conference

Asia Risk Congress

product

CrossAsset - Leading the Industry in Advanced Models and Methods

content collection

Numerix Quant Tech Resource Hub

on-demand webinar

SRP Europe Conference 2021: Optimizing Financial Valuations to Improve Investor Experience

on-demand webinar

QuantMinds 2020: Modelling Energy Curves for XVA

conference

QuantMinds in Focus

on-demand webinar

Quantitative R&D Innovations Update

on-demand webinar

Neural Networks with Asymptotics Control

quantitative research

Machine Learning: Deep Asymptotics