Analytical formulas for a local volatility model with stochastic rates

Abstract

This paper presents new approximation formulae for European options in a local volatility model with stochastic interest rates. This is a companion paper to our work on perturbation methods for local volatility models [Int. J. Theor. Appl. Finance, 2010, 13(4), 603–634] for the case of stochastic interest rates. The originality of this approach is to model the local volatility of the discounted spot and to obtain accurate approximations with tight estimates of the error terms. This approach can also be used in the case of stochastic dividends or stochastic convenience yields. We finally provide numerical results to illustrate the accuracy with real market data.

Keywords:

• Computational finance
• Option pricing
• Interest rates
• Equity options
• Mathematics of finance
• Multi-factor models
• Stochastic analysis

Acknowledgements

The second author is grateful to the Chair Financial Risks of the Risk Foundation and to the University Joseph Fourier for financial support (MSTIC grant entitled REFINE). A significant part of this work was done when the second author was at the Grenoble Institute of Technology.