LIBOR市场模型的平均场推广

IF 0.5 Q4 BUSINESS, FINANCE

International Journal of Theoretical and Applied Finance Pub Date : 2021-09-22 DOI:10.1142/S0219024922500054

Sascha Desmettre, Simon Hochgerner, Sanela Omerovic, S. Thonhauser

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引用次数: 1

摘要

我们引入了LIBOR市场模型(LMM)的平均场扩展，该扩展保留了原始模型的基本特征。其中，这些特征是鞅性，可直接实现的校准和经济上合理的经典LMM参数化。同时，平均场LIBOR市场模型(MF-LMM)旨在降低爆炸情景的可能性，特别是在长期担保的市场一致估值中产生的可能性。为此，我们证明了相应的MF-LMM的存在唯一性，并研究了它的实用方面，包括Black '76型公式。此外，我们还对MF-LMM进行了广泛的数值分析。相应的蒙特卡罗方法是基于一个合适的相互作用粒子系统，它近似于底层的平均场方程。

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A Mean-Field Extension of the LIBOR Market Model

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.

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来源期刊

International Journal of Theoretical and Applied Finance BUSINESS, FINANCE-

CiteScore

1.10

自引率

20.00%

发文量

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.