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Skew Ornstein–Uhlenbeck processes with sticky reflection and their applications to bond pricing

Part of: Distribution theory - Probability Stochastic analysis Markov processes

Published online by Cambridge University Press:  06 March 2024

Shiyu Song  and
Guangli Xu
Shiyu Song*
Affiliation:
Weifang University
Guangli Xu*
Affiliation:
University of International Business and Economics
*
*Postal address: School of Mathematics and Statistics, Weifang University, Weifang, 261061, China. Email: shiyu.song@wfu.edu.cn
**Postal address: School of Statistics, University of International Business and Economics, Beijing, 100029, China. Email: xuguangli@uibe.edu.cn
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Abstract

We study a skew Ornstein–Uhlenbeck process with zero being a sticky reflecting boundary, which is defined as the weak solution to a stochastic differential equation (SDE) system involving local time. The main results obtained include: (i) the existence and uniqueness of solutions to the SDE system, (ii) the scale function and speed measure, and (iii) the distributional properties regarding the transition density and the first hitting times. On the application side, we apply the process to interest rate modeling and obtain the explicit pricing formula for zero-coupon bonds. Numerical examples illustrate the impacts on bond yields of skewness and stickiness parameters.

Keywords

Skew Ornstein–Uhlenbeck processsticky reflectionGreen functionfirst hitting timezero-coupon bond

MSC classification

Primary: 60J60: Diffusion processes
Secondary: 60E05: Distributions 60H10: Stochastic ordinary differential equations

Information

Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 4 , December 2024 , pp. 1172 - 1195
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust

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