The risk-neutral stochastic volatility in interest rate models with jump-diffusion processes

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:347

Article

Martinez-Rodriguez, J.¹ 

[1] Univ Valladolid, Fac Ciencias Econ & Empresariales, Dept Econ Aplicada, Ave Valle Esgueva 6, E-47011 Valladolid, Spain

关键词: Interest rate model;    Jump-diffusion stochastic processes;    Stochastic volatility;    Risk-neutral measure;    Numerical differentiation;    Nonparametric estimation;   

DOI  :  10.1016/j.cam.2018.07.048

来源: Elsevier

【 摘 要 】

In this paper, we consider a two-factor interest rate model with stochastic volatility and we propose that the interest rate follows a jump-diffusion process. The estimation of the market price of risk is an open question in two-factor jump-diffusion term structure models when a closed-form solution is not known. We prove some results that relate the slope of the yield curves, interest rates and volatility with the functions of the processes under the risk-neutral measure. These relations allow us to estimate all the functions with the bond prices observed in the markets. Moreover, the market prices of risk, which are unobservable, can be easily obtained. Then, we can solve the pricing problem. An application to US Treasury Bill data is illustrated and a comparison with a one-factor model is shown. Finally, the effect of the change of measure on the jump intensity and jump distribution is analysed. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free