Markov-modulated jump-diffusion models for the short rate: Pricing of zero coupon bonds and convexity adjustment

被引：1
|
作者：
Lopez, Oscar [1 ]
Oleaga, Gerardo [2 ]
Sanchez, Alejandra [1 ,3 ]
机构：
[1] Univ Nacl Colombia, Dept Matemat, Bogota, Colombia
[2] Univ Complutense Madrid, Dept Anal Matemat & Matemat Aplicada, Madrid, Spain
[3] Univ Complutense Madrid, Fac Ciencias Matemat, Madrid, Spain
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2021年 / 395卷
关键词：
Markov-modulated jump-diffusion model; Short rate model; Jump-telegraph process; Unbiased expectation hypothesis; Convexity adjustment; Bond valuation; TERM STRUCTURE;
D O I：
10.1016/j.amc.2020.125854
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this article, we consider a Markov-modulated model with jumps for the short rate. Using the main properties of a telegraphic process with jumps we compute the expected short rate. We obtain closed formulas for the zero coupon bond price assuming the Unbiased Expectation Hypothesis for the forward rates. Next, we obtain the coupled system of partial differential equations for the bond price using only no-arbitrage arguments. Numerical solutions are provided for some selected examples. The results obtained from both methods are compared and allow to estimate the magnitude of the convexity-adjustment. (c) 2020 Elsevier Inc. All rights reserved.
引用
收藏
页数：14
相关论文
共 30 条
  • [1] Variance Swap Pricing under Markov-Modulated Jump-Diffusion Model
    Liu, Shican
    Yang, Yu
    Zhang, Hu
    Wu, Yonghong
    [J]. DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2021, 2021
  • [2] Option pricing under a Markov-modulated Merton jump-diffusion dividend
    Shan, Yuanchuang
    Yi, Haoran
    Zhang, Xuekang
    Shu, Huisheng
    [J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2023, 52 (05) : 1490 - 1506
  • [3] Pricing options under a generalized Markov-modulated jump-diffusion model
    Elliott, Robert J.
    Siu, Tak Kuen
    Chan, Leunglung
    Lau, John W.
    [J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2007, 25 (04) : 821 - 843
  • [4] Optimal Investment for the Insurers in Markov-Modulated Jump-Diffusion Models
    Jinzhi Li
    Haiying Liu
    [J]. Computational Economics, 2015, 46 : 143 - 156
  • [5] Optimal Investment for the Insurers in Markov-Modulated Jump-Diffusion Models
    Li, Jinzhi
    Liu, Haiying
    [J]. COMPUTATIONAL ECONOMICS, 2015, 46 (01) : 143 - 156
  • [6] PRICING VULNERABLE OPTIONS UNDER A MARKOV-MODULATED JUMP-DIFFUSION MODEL WITH FIRE SALES
    Yang, Qing-Qing
    Ching, Wai-Ki
    He, Wanhua
    Siu, Tak-Kuen
    [J]. JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2019, 15 (01) : 293 - 318
  • [7] Convexity preserving jump-diffusion models for option pricing
    Ekstrom, Erik
    Tysk, Johan
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 330 (01) : 715 - 728
  • [8] Pricing vulnerable options under cross-asset markov-modulated jump-diffusion dynamics
    Lian, Yu -Min
    Chen, Jun -Home
    [J]. INTERNATIONAL REVIEW OF ECONOMICS & FINANCE, 2024, 94
  • [9] Pricing participating products with Markov-modulated jump-diffusion process: An efficient numerical PIDE approach
    Fard, Farzad Alavi
    Siu, Tak Kuen
    [J]. INSURANCE MATHEMATICS & ECONOMICS, 2013, 53 (03): : 712 - 721
  • [10] Risk-minimizing option pricing under a Markov-modulated jump-diffusion model with stochastic volatility
    Su, Xiaonan
    Wang, Wensheng
    Hwang, Kyo-Shin
    [J]. STATISTICS & PROBABILITY LETTERS, 2012, 82 (10) : 1777 - 1785
123