Analytical Formulas for Pricing CMS Products in the LMM with Stochastic Volatility
In this paper, we develop a series of approximations for a fast analytical pricing of European constant maturity swap (CMS) products, such as CMS swaps, CMS caps/floors, and CMS spread options, for the LIBOR Market Model (LMM) with stochastic volatility. The derived formulas can also be used for model calibration to the market, including European swaptions and CMS products.
The first technical achievement of this work is related to the optimal calculation of the measure change. For single-rate CMS products, we have used the standard linear regression of the measure change, with optimally calculated coefficients. For the CMS spread options, where the linear procedure does not work, we propose a new effective non-linear measure change technique. The fit quality of the new results is confirmed numerically using Monte Carlo simulations. The second technical advance of the article is a theoretical derivation of the generalized spread option price via two-dimensional Laplace transform presented in a closed form in terms of the complex Gamma-functions.
Authors: Alexandre Antonov and Matthieu Arneguy
In this paper, we develop a series of approximations for a fast analytical pricing of European constant maturity swap (CMS) products, such as CMS swaps, CMS caps/floors, and CMS spread options, for the LIBOR Market Model (LMM) with stochastic volatility. The derived formulas can also be used for model calibration to the market, including European swaptions and CMS products.
The first technical achievement of this work is related to the optimal calculation of the measure change. For single-rate CMS products, we have used the standard linear regression of the measure change, with optimally calculated coefficients. For the CMS spread options, where the linear procedure does not work, we propose a new effective non-linear measure change technique. The fit quality of the new results is confirmed numerically using Monte Carlo simulations. The second technical advance of the article is a theoretical derivation of the generalized spread option price via two-dimensional Laplace transform presented in a closed form in terms of the complex Gamma-functions.
Authors: Alexandre Antonov and Matthieu Arneguy
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.
