JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (3): 1-11.doi: 10.6040/j.issn.1671-9352.0.2023.295

• Financial Mathematics •     Next Articles

Pricing quotient options by the moment matching approach under the Hull-White model

ZHANG Lidong1, WU Shuimiao2, TIAN Jinghe2, DONG Yilin2, MENG Xiangbo1*   

  1. 1. School of Science, Tianjin University of Science and Technology, Tianjin 300457, China;
    2. College of Economics and Management, Tianjin University of Science and Technology, Tianjin 300457, China
  • Published:2025-03-10

PDF (PC)

90

Abstract: Under the assumption that the underlying asset price follows the mean reversion process, the quotient option pricing problem under the Hull-White model is studied by using the moment matching technique. Compared with the Monte Carlo simulation method, the stability and efficiency of quotient option pricing can be significantly improved by the proposed valuation method, while maintaining accuracy. Furthermore, in the Chinese stock market, the stocks of two leading companies are chosen as research objects for evaluating the applicability of the option pricing model in the financial market. The results indicate that the estimation results of this model and the Monte Carlo simulation method exhibit minimal differences, althougth the former requires significantly less time.

Key words: quotient option, mean-reverting process, Hull-White model, moment matching

CLC Number: 

  • O211
[1] 王波,朱顺伟,邓亚东,等. 4/2随机波动率模型下的期权定价[J]. 系统管理学报, 2020, 29(1):192-198. WANG Bo, ZHU Shunwei, DENG Yadong, et al. Options on S& P 500 index by fundamental transform approach: 4/2 stochastic volatility model[J].Journal of System Management, 2020, 29(1):192-198.
[2] SHI Chao. Asymptotic analysis of the Heston model and its statistical and financial applications[J]. Applied Stochastic Models in Business and Industry, 2022, 38(6):1049-1060.
[3] SHI Z, ALFONZETTI S. Solving parametric volterra integral equation from distributed-order rough heston model and option pricing[J]. Mathematical Problems in Engineering, 2022, 2022:1979003.
[4] ZHANG Qi, SONG Haiming, HAO Yongle. Semi-implicit FEM for the valuation of American options under the Heston model[J]. Computational and Applied Mathematics, 2022, 41(2):73.
[5] HULL J C, WHITE A. The pricing of options on assets with stochastic volatilities[J]. The Journal of Finance, 1987, 42(2):281-300.
[6] HULL J. An analysis of the bias in option pricing caused by a stochastic volatility[J]. Advances in Futures and Options Research, 1988, 3:29-61.
[7] LI Xun, WU Zhenyu. On an approximation method for pricing a high-dimensional basket option on assets with mean-reverting prices[J]. Computers & Operations Research, 2008, 35(1):76-89.
[8] YU Bo, ZHU Hongmei, WU Ping. The closed-form approximation to price basket options under stochastic interest rate[J]. Finance Research Letters, 2022, 46:102434.
[9] WU Ping, LIN Hui. Pricing of basket options by conditioning and moment matching[J]. The Journal of Derivatives, 2020, 28(2):80-87.
[10] GAO Zhichao, WANG Xiaosheng, HA Mingyu. Multi-asset option pricing in an uncertain financial market with jump risk[J]. Journal of Uncertainty Analysis and Applications, 2016, 4(1):1.
[11] 李敬楠,刘会利. 随机利率下基于O-U过程的商期权定价[J]. 吉首大学学报(自然科学版),2022,43(2):23-30. LI Jingnan, LIU Huili. Quotientoption pricing based on O-U process with stochastic interest rate[J]. Journal of Jishou University(Natural Sciences Edition), 2022, 43(2):23-30.
[12] ÖZSOY A U. Pricing and hedging of quotient options in(·overI)stanbul stock exchange[D]. Ankara: Middle East Technical University, 2016.
[13] BOS L P, WARE A F, PAVLOV B S. On a semi-spectral method for pricing an option on a mean-reverting asset[J]. Quantitative Finance, 2002, 2(5):337-345.
[14] HULL J C, WHITE A D. Numerical procedures for implementing term structure models I: single-factor models[J]. The Journal of Derivatives, 1994, 2(1):7-16.
[15] HULL J, WHITE A. Numerical procedures for implementing term structure models II: two-factor models[J]. Journal of Derivatives, 1994, 2(2):37-48.
[16] VASICEK O. An equilibrium characterization of the term structure[J]. Journal of Financial Economics, 1977, 5(2): 177-188.
[17] COX J C, INGERSOLL J E, ROSS S A. A re-examination of traditional hypotheses about the term structure of interest rates[J]. The Journal of Finance, 1981, 36(4):769-799.
[18] COX J C, INGERSOLL J E, ROSS S A. A theory of the term structure of interest rates[J]. Econometrica, 1985, 53(2): 385.
[19] ZHU Y L, WU X N, CHERN I L. Derivative securities and difference methods[M]. New York: Springer, 2004.
[20] SEYDEL R. Tools for computational finance[M]. 3rd ed. Berlin: Springer, 2006.
[21] BROADIE M, GLASSERMAN P. A stochastic mesh method for pricing high-dimensional American options[J]. Journal of Computational Finance, 2004, 7(4):35-72.
[1] Pingtao LYU,Caishi WANG,Jijun ZHAO. A class of two-state quantum walk based on Hadamard walk with the same eigenvalues and continuous spectrum [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(8): 84-93.
[2] Yufeng GAO,Decheng FENG. Upcrossing and downcrossing inequalities for conditional demimartingales and conditional N-demimartingales [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(6): 122-126.
[3] Yaru ZHANG,Li XIA,Dianqiu ZHANG. Perpetual American lookback option pricing under mixed bi-fractional Brownian motion [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 98-107.
[4] Xiaodong YAN. Strategic limit theory and strategic statistical learning [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(1): 1-10, 45.
[5] Chenghao XU,Kaiyong WANG. The ruin probability of a two-dimensional discrete-time risk model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(11): 27-34, 52.
[6] Peng YANG,Xiaoyan ZHANG. Optimal reinsurance contract design based on Stackelberg game [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(11): 1-14,26.
[7] Shimiao ZHANG,Yan LYU. Parameter estimation for competitive Lotka-Volterra model with Lévy noise [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(10): 24-31.
[8] Jiaxin DING,Yongfeng GUO,Lina MI. Transition behavior of underdamped periodic potential system driven by Gaussian noise and Lévy noise [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 111-117.
[9] Qi GAO,Hongshuai DAI,Yanhua WU. MPEWMA chart for detecting tandem queuing network [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 104-110, 117.
[10] Yejun CHEN,Huisheng DING. θ-almost periodic solutions for stochastic differential equations in infinite dimensions with Stepanov almost periodic coefficients [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(6): 113-126.
[11] LI Yong-ming, NIE Cai-ling, LIU Chao, GUO Jian-hua. Consistency of estimator of nonparametric regression function for arrays of rowwise NSD [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 69-74.
[12] CHEN Hao-jun, ZHENG Ying, MA Ming, BIAN Li-na, LIU Hua. Covariance of self-exciting filtered Poisson process [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 75-79.
[13] ZHOU Yu-lan, LI Zhuan, LI Xiao-hui. Properties of modified stochastic gradient operators in continuous-time Guichardet-Fock space [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 62-68.
[14] XIAO Xin-ling. Forward-backward stochastic differential equations on Markov chains [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 46-54.
[15] CHEN Li, LIN Ling. Stock option pricing with time delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 36-41.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] DIAO Ke-feng and ZHAO Ping . On the coloring of C-hypergraphs with minimum connected pair graphs[J]. J4, 2007, 42(2): 56 -58 .
[2] XUE Yan-Bei, YANG Bei, CHEN Zhen-Xiang. Structural health monitoring of civil engineering based on wavelet analysis[J]. J4, 2009, 44(9): 28 -31 .
[3] JIANG Xue-lian, SHI Hong-bo*. The learning algorithm of a generative and discriminative combination classifier[J]. J4, 2010, 45(7): 7 -12 .
[4] PENG Yan-fen,LI Bao-zong,LIU Tian-bao . Relationships between the structures and the anesthetic[J]. J4, 2006, 41(5): 148 -150 .
[5] YANG Lun, XU Zheng-gang, WANG Hui*, CHEN Qi-mei, CHEN Wei, HU Yan-xia, SHI Yuan, ZHU Hong-lei, ZENG Yong-qing*. Silence of PID1 gene expression using RNA interference in C2C12 cell line[J]. J4, 2013, 48(1): 36 -42 .
[6] LIU Yan-ping, WU Qun-ying. Almost sure limit theorems for the maximum of Gaussian sequences#br# with optimized weight[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(05): 50 -53 .
[7] DU Ji-xiang1,2, YU Qing1, ZHAI Chuan-ming1. Age estimation of facial images based on non-negative matrix factorization with sparseness constraints[J]. J4, 2010, 45(7): 65 -69 .
[8] Ming-Chit Liu. THE TWO GOLDBACH CONJECTURES[J]. J4, 2013, 48(2): 1 -14 .
[9] WANG Kai-rong, GAO Pei-ting. Two mixed conjugate gradient methods based on DY[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 16 -23 .
[10] WU Dai-yong, ZHANG Hai. Stability and bifurcation analysis for a single population discrete model with Allee effect and delay[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(07): 88 -94 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd