Linearized Hamiltonian of the LIBOR market model: analytical and empirical results

ABSTRACT

The linearized Hamiltonian model is proposed to extend the London Interbank Offered Rate (LIBOR) Market Model (LMM). Firstly, we studied the Hamiltonian of LMM in the framework of quantum finance, and the nontrivial upper triangle form of LIBOR drift is derived. The linearized Hamiltonian is derived to improve the explanatory capability of the model for market data. Our approach uses one more parameter to explain the initial condition and the model can be used to calibrate LIBORs with extremely high accuracy. Furthermore, the market time index is required for applying the model to multi-LIBOR, and the results imply that the LIBOR future time lattice becomes shorter as one goes from near future to distant future.

KEYWORDS:

• LIBOR market model
• interest rate models
• quantitative finance
• quantum finance

JEL CLASSIFICATION:

• E43
• E47

Notes

¹ The probability distribution of data is plotted by dividing [min max] ϕ_I to 30 intervals. The number of ϕ_I is recorded in each interval. Here, we have four LIBORs and the axes of ϕ_I, $I=1,2,3,4$ should be different. In the graph, the LIBOR ϕ_I, $I=1$ is used as the axis. The other three axes of ϕ_I, $I=2,3,4$ have the similar value and are not plotted on the graph.

Additional information

Funding

The authors gratefully acknowledge the financial support from the National Natural Science Foundation of China [No. 71401031], [No. 71273048], [No. 71473036]; the Humanity and Social Science Youth Foundation of Ministry of Education of China [No. 14YJC790110]; the Social Science Foundation of Jiangsu Province [No. 3214004405]; the Doctoral Agglomeration Plan of Jiangsu Province [No. 1114000242]; the National Social Science Foundation of China [No. 15CGL045]; the Ministry of Education of Jiangsu Province [No. 2014SJD013].