Sascha Desmettre, Simon Hochgerner, Sanela Omerovic, S. Thonhauser
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We introduce a mean-field extension of the LIBOR market model (LMM) which preserves the basic features of the original model. Among others, these features are the martingale property, a directly implementable calibration and an economically reasonable parametrization of the classical LMM. At the same time, the mean-field LIBOR market model (MF-LMM) is designed to reduce the probability of exploding scenarios, arising in particular in the market-consistent valuation of long-term guarantees. To this end, we prove existence and uniqueness of the corresponding MF-LMM and investigate its practical aspects, including a Black '76-type formula. Moreover, we present an extensive numerical analysis of the MF-LMM. The corresponding Monte Carlo method is based on a suitable interacting particle system which approximates the underlying mean-field equation.
期刊介绍：
The shift of the financial market towards the general use of advanced mathematical methods has led to the introduction of state-of-the-art quantitative tools into the world of finance. The International Journal of Theoretical and Applied Finance (IJTAF) brings together international experts involved in the mathematical modelling of financial instruments as well as the application of these models to global financial markets. The development of complex financial products has led to new challenges to the regulatory bodies. Financial instruments that have been designed to serve the needs of the mature capitals market need to be adapted for application in the emerging markets.
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