Table of Content

  

20 March 2025
Volume 60 Issue 3

Financial Mathematics


Financial Mathematics

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

ZHANG Lidong, WU Shuimiao, TIAN Jinghe, DONG Yilin, MENG Xiangbo

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

Abstract ( 134 )   PDF (470KB) ( 99 )   Save

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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.

Double-triggered catastrophe put option with risk ratio and its pricing

LI Shilong, LIU Xi

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(3):  12-21.  doi:10.6040/j.issn.1671-9352.0.2023.231

Abstract ( 55 )   PDF (3699KB) ( 67 )   Save

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In order to reflect both the impact of the accumulated catastrophe compensation loss of insurance companies on the exercise returns of catastrophe options and the risk tolerance level of insurance companies, the risk ratios based on VaR is added into the payment structure of ordinary double triggered catastrophe put options. Firstly, the pricing formula for catastrophe put options with risk ratios is derived in the product probability space of finance and catastrophe; Secondly, the POT model is utilized to fit the distribution of catastrophe loss based on the typhoon catastrophe data in China to display the thick tailed characteristics of catastrophic losses; Finally, the Monte Carlo simulation method is used to analyze the sensitivity of the factors affecting the catastrophe put option and the prices of the catastrophe put options with risk ratios are compared with those of ordinary catastrophe options.

Vulnerable European option pricing in a regime-switching and Hawkes jump diffusion model

DU Huiyuan, FAN Xiaoming

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(3):  22-32.  doi:10.6040/j.issn.1671-9352.0.2024.105

Abstract ( 70 )   PDF (3014KB) ( 46 )   Save

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Option pricing with counterparty default risk under stochastic volatility and stochastic interest rate models is studied. In this model, the mean reversion levels of volatility and interest rate process are controlled by a continuous Markov process in a finite state space, and it is assumed that both the underlying asset price process and the counterparty asset price process contain jumps, and their jumps obey the Hawkes process with self-stimulation, and it is assumed that the volatility process also contains jumps. The analytical pricing formula of European vulnerable option is derived by means of measure transform, solution of discount characteristic function and multivariate Fourier transform. Then the fast Fourier transform method is used to calculate the effective approximation of the option analytic pricing formula, and the accuracy of the approximation is verified by Monte Carlo simulation. Finally, the sensitivity of different parameters in the proposed model to the price of vulnerable call options is analyzed, and the difference between the proposed model and the stochastic interest rate model without Markov regime-switching(MRS)is compared by numerical experiments, and the impact of the introduction of regime-switching in the model on the option pricing results is illustrated.

Stochastic volatility analysis of interest rate based on MCMC model

HAN Qi, XIA Xinzhou

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(3):  33-40.  doi:10.6040/j.issn.1671-9352.0.2023.163

Abstract ( 59 )   PDF (6949KB) ( 49 )   Save

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Currently, researches on the interest rate volatility index are constructed on the basis of the interest rate derivative price model. To further expand the application scope of the implied interest rate volatility index, the properties of the stochastic volatility implied in the yield data information are studied on the basis of the interest rate volatility model. Based on the yield data of government bonds from January 2021 to February 2023, the yield data are modeled and analyzed by the Markov chain Monte Carlo(MCMC)model. The results show that the volatility of the long-term interest rate is significantly lower than that of the short-term interest rate. Because this paper uses the treasury bond yield as the basic data, compared with the volatility index in the option market, the model in this paper is not affected by the type and scale of options in the option market and has a greater range of application.

Efficiency of stock index market based on improved recurrence plot

LIU Guidong, KE Yilong, YOU Guoqiao, LIU Manxi

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(3):  41-48.  doi:10.6040/j.issn.1671-9352.0.2023.526

Abstract ( 60 )   PDF (4047KB) ( 38 )   Save

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An enhanced computational model is introduced for the entropy based on recurrence microstates(ENRM), which builds upon the original method and employs an improved approach involving the traversal of submatrices using a rolling window. This improved computational model significantly improves computational efficiency while maintaining the accuracy of the original algorithm. For simulation experiments, a logistic model is employed, and the results prove that this improved computational model has higher computational efficiency and accuracy. Furthermore, research findings on market efficiency suggest that using the entropy based on recurrence microstates(ENRM)in combination with the traditional recurrence plot metric, entropy(ENTR), not only retains the ability of ENTR to quantify market efficiency but also effectively identifies and analyzes periods during which market efficiency undergoes dynamic evolution.

Optimal investment and benefit payment adjustment strategy for target benefit pension plan under 4/2 stochastic volatility model

HAN Jingyi, CHANG Hao, CHEN Zhen

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(3):  49-59.  doi:10.6040/j.issn.1671-9352.0.2023.436

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The target benefit pension(TBP)plan under 4/2 stochastic volatility model contains both the active members and the retired members, where the active members pay predetermined contributions to the pension fund and the retired members receive a corresponding pension from the fund, and the benefit payment level of the retired members depends on the investment situation. It is assumed that the pension fund can be invested in a risk-free asset and a stock, and the stock price follows the 4/2 stochastic volatility model. Applying the stochastic optimal control theory, explicit solutions for the optimal investment and benefit payment adjustment strategy are derived, and a numerical example is given to illustrate the results obtained. Methodological and theoretical support for solving other complex investment problems in a stochastic volatility environment, and the reference basis for asset allocation and risk management of fund managers are provided.

European option pricing under double Heston jump-diffusion model with generalized fractional Brownian motion

ZHANG Zhaoliu, FAN Xiaoming

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(3):  60-68.  doi:10.6040/j.issn.1671-9352.0.2024.277

Abstract ( 60 )   PDF (2191KB) ( 52 )   Save

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First, a double Heston jump-diffusion model based on generalized fractional Brownian motion is proposed under the risk-neutral probability measure, and the corresponding European call option pricing formula of the model is introduced by solving the partial differential equation system of the characteristic function. The Monte Carlo simulation verifies the accuracy of the European option pricing formula. The rationality and effectiveness of the established option pricing model are verified by numerical analysis, and the influence of generalized fractional Brownian motion parameter H and volatility on option price is discussed.

Estimation and application of the change-point quantile regression model based on linearization technique

ZHOU Xiaoying, JI Chen, TU Xiaoyi

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(3):  69-76.  doi:10.6040/j.issn.1671-9352.0.2024.084

Abstract ( 59 )   PDF (828KB) ( 50 )   Save

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The change-point quantile regression model constructed by the intersection of a straight line and a quadratic curve at a change point. This model can flexibly handle change point data and capture the overall distribution of the response variable. Due to the presence of the change point parameter, the models loss function is non-convex, which is a challenge for parameter estimation. To address this issue, the loss function is linearized based on the linearization technique combining with an iterative algorithm, which can simultaneously estimate the change point and other parameters. The interval estimation theory for the estimators is also derived. Numerical simulation results indicate that the proposed estimation method exhibits good consistency and effectiveness. Empirical analysis of per capita GDP and power quality data further verifies the feasibility and practicality of the proposed model and method.

Least squares estimator of the first-order and mildly explosive autoregression with mixing errors

DUAN Ticheng, XU Chengkai, LU Zijie, JIA Peiyan, XIE Suya, YANG Wenzhi

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(3):  77-87.  doi:10.6040/j.issn.1671-9352.0.2023.439

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The least squares(LS)estimator is studied for the first-order and mildly explosive autoregression with φ-mixing errors. Under some weak conditions of E(u1)=0, E(|u1|4)<∞ and φ(n)=O(n^-8), the limit distribution of standard Cauchy distribution is obtained for the LS estimator. Some simulations are given, which agree with the theory results. As an application, the first-order mildly explosive model and autoregressive coefficient interval estimation are used to study the growth process of share price for the NVIDIA corporation common stock from 2013 to 2023.

Composite quantile regression estimation of linear mixed effects model

LI Jing, YANG Yiping, ZHAO Peixin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(3):  88-99.  doi:10.6040/j.issn.1671-9352.0.2023.226

Abstract ( 57 )   PDF (2769KB) ( 40 )   Save

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Considering the robust estimation problem of linear mixed effect model, a composite quantile regression estimation method based on orthogonal projection is proposed by combining the QR decomposition technique of matrix and the composite quantile regression method. The random effects are eliminated by QR decomposition technique, and then the fixed effects are estimated by constructing the composite quantile regression objective function. Under some regular conditions, the asymptotic normality of the proposed estimates is proved. The proposed estimation method does not need to make any restrictive assumptions about the distribution of model errors and random effects, and the estimates of fixed effects are not affected by random effects. Further, the simulation study compares the proposed method with the orthogonality-based estimation of moment method, which shows that the proposed method is robust and applied to the actual data analysis.

Partially functional linear quantile regression model and its application for incomplete observations

YANG Yujie, LING Nengxiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(3):  100-106.  doi:10.6040/j.issn.1671-9352.0.2024.051

Abstract ( 69 )   PDF (3044KB) ( 77 )   Save

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Firstly, based on incomplete observed functional data, partially functional linear quantile regression model, the estimation method and prediction step are introduced. Secondly, due to the widespread existence of incomplete observed functional variables, the mast records every 10 minutes from April 8, 2019 to August 31, 2020 in Nepal for empirical analysis are used. Aiming at the incomplete functional characteristics of wind speed data, an incomplete partial functional linear quantile regression model with daily mean air pressure as the response variable is constructed, and the estimators of the unknown slope function and unknown parameters of the model are obtained, and the daily mean air pressure is predicted and analyzed, which further illustrates the effectiveness of the model and the method.

Test of parameter change point in RCA(1)model based on LSCUSUM method

HOU Chengting, CHEN Zhanshou

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(3):  107-115.  doi:10.6040/j.issn.1671-9352.0.2023.541

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The parameter change point problem of the first-order random coefficient autoregressive(RCA(1))model is studied, and a location and scale based cumulative sum(LSCUSUM)test statistic is proposed to test the parameter change points. Under the null hypothesis of no change points, the convergence of the LSCUSUM statistic to the upper bound of the Brownian bridge is derived. Consistency of the method is established under the alternative hypothesis. Numerical simulation results demonstrate that the introduced LSCUSUM method effectively controls the empirical level. Furthermore, compared to existing methods for testing parameter change points in RCA(1)models, the proposed approach exhibits an enhanced empirical power. Finally, the method is applied to analyze daily closing data of Dongjing electronics stock, and detect the change points within the dataset.

Bayesian parametric estimations for spatial error models based on slice-Gibbs sampling

LI Aogui, ZHAO Yuanying

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(3):  116-126.  doi:10.6040/j.issn.1671-9352.0.2023.474

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A Markov chain Monte Carlo(MCMC)technique called the slice-Gibbs sampling algorithm is proposed to calculate joints Bayesian estimations of unknown parameters for spatial error models, the proposed algorithm and Bayesian approach are illustrated by two simulation studies, the model and methodology are demonstrated by a real example.