Projection on a Quadratic Model by Asymptotic Expansion with an Application to LMM Swaption
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
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
Authors
Dr. Alexandre Antonov
Dr. Antonov received his PhD degree from the Landau Institute for Theoretical Physics in 1997 and joined Numerix in 1998, where he currently works as a Senior Vice President of Quantitative Research. His activity is concentrated on modeling and numerical methods for interest rates, cross currency, hybrid, credit and CVA. Dr. Antonov is a published author for multiple publications in mathematical finance, including RISK magazine and a frequent speaker at financial conferences.
