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American Option Valuation Under the Framework of CGMY Model with regime-switching process

COMPUTATIONAL ECONOMICS 2024年 1-25页

作者： Fan, Congyin Gu, Xian-Ming Dong, Shuhong Yuan, Hua Guizhou Univ Commerce Sch Econ & Finance Guiyang 550014 Guizhou Peoples R China Southwestern Univ Finance & Econ Sch Math Chengdu 611130 Sichuan Peoples R China

In this paper, the values and optimal exercise prices of American option under the CGMY model with regime-switching process are considered. For this case, the pricing mathematical model is a free boundary problem which includes d coupled fractional partial differential equations (PDEs) in one dimension with free boundary conditions, d denoting the number of regimes of financial market. The above problem is changed as a fixed one by adding a nonlinear penalty term to each fractional PDE. After the finite difference method is set to solve the transformed model, unlike the conventional method, the discretized coupling system is reformulated by expanding dimensions such that numerical results in all states can be calculated simultaneously. Finally, significant effects of the parameters in our model on the option exercise price are verified through our selected numerical results. Meanwhile, the curves of Delta and Gamma are reported to show feasibility of our model and the proposed numerical method.

关键词： CGMY model regime-switching process American option Fractional derivatives

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Implicit-explicit Runge-Kutta methods for pricing financial derivatives in state-dependent regime-switching jump-diffusion models

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2024年第2期70卷 1601-1632页

作者： Maurya, Vikas Singh, Ankit Rajpoot, Manoj K. Rajiv Gandhi Inst Petr Technol Dept Math Sci Math & Comp Lab Amethi 229304 UP India

In this paper, we have devised a novel class of implicit-explicit Runge-Kutta methods for the valuation of financial derivatives under state-dependent regime-switching jump-diffusion models. The developed methods utilize an implicit technique to solve the problem without performing inversion of the coefficient matrix at each state of the economy. The pricing of European options under the regime-switching jump-diffusion process is formulated by coupled partial integro-differential equations, whereas the pricing framework for American options is based on addressing coupled linear complementary problems. The operator splitting technique is employed along with implicit-explicit methods to solve the linear complementarity problems. Consistency and convergence results of the developed methods are theoretically established using the discrete l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell <^>switching$$\end{document}-norm. The accuracy and efficiency of developed methods are validated by solving the European and American options at different states of the economy under regime-switching jump-diffusion models. Finally, the computed results are compared with the recently proposed methods mentioned in the literature.

关键词： regime-switching process Partial integro-differential equations Implicit-explicit methods Operator splitting Stability analysis European and American options

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regime-switching constrained viscosity solutions approach for controlling dam-reservoir systems

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2020年第9期80卷 2057-2072页

作者： Yoshioka, Hidekazu Yoshioka, Yumi Shimane Univ Grad Sch Nat Sci & Technol Nishikawatsu Cho 1060 Matsue Shimane 6908504 Japan

A new stochastic control problem of a dam-reservoir system installed in a river is analyzed both mathematically and numerically. Water balance dynamics of the reservoir are piece-wise deterministic and are driven by a stochastic regime-switching inflow process. The system is controlled to balance among the operation purpose and the internal and downstream environmental conditions. Finding the optimal operation policy of the system reduces to solving an optimality equation with a discontinuous Hamiltonian, which is a system of nonlinear degenerate parabolic (or hyperbolic) equations. We show that the optimality equation has at most one constrained viscosity solution and find the solution explicitly under certain conditions. The model is applied to numerical computation of the operation policy of an existing dam-reservoir system using a high-order finite difference scheme. The computational results can suggest how the operation policy should be adapted according to the environmental concerns of the river. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Stochastic optimal control regime-switching process Dam-reservoir system Constrained viscosity solution Finite difference discretization

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Exploring the price dynamics of CO₂ emissions allowances in China's emissions trading scheme pilots

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ENERGY ECONOMICS 2017年 67卷 213-223页

作者： Chang, Kai Pei, Ping Zhang, Chao Wu, Xin Nanjing Univ Sch Business Nanjing 210093 Jiangsu Peoples R China Zhejiang Univ Finance & Econ Sch Finance Hangzhou 310038 Zhejiang Peoples R China Ctr Res Regulat & Policy Zhejiang Prov Hangzhou 310018 Peoples R China Zhejiang Univ Finance & Econ China Acad Financial Res Hangzhou 310038 Zhejiang Peoples R China Zhejiang Univ Finance & Econ Collaborat Innovat Ctr Local Finance Hangzhou 310038 Zhejiang Peoples R China

Establishing regional emissions trading scheme pilots in China is a newly transformative and explorative practice. In this paper, we examine the spot price dynamics, asymmetric clustering and regime-switching behaviors of CO2 emissions allowances in the new China-wide emissions trading scheme (CETS) pilots using AR-GARCH, AR-TARCH and MRS-AR-GARCH models. The regional ETS pilots' design in China vary widely in their coverage thresholds, sector coverage, emissions allocation and caps setting methods, market trading rules and price stabilization provisions. Our empirical results indicate that the spot prices of regional emissions allowances exhibit significant dynamic behaviors, asymmetric leverage effects and regime-switching behaviors in the entire period considered;previous market overreactions in the Beijing, Tianjin and Guangdong pilots have stronger price clustering effects on future conditional variances than do the Shanghai and Hubei pilots. Unexpected market shocks and greater persistence in the Beijing, Tianjin and Guangdong ETS pilots display stronger market volatility and higher market risks, and their asymmetric leverage effects display a decreasing trend in the volatility of the BEA, TJEA and GDEA prices. The BEA and SHEA prices exhibit significant regime-switching behaviors, price jumps and higher volatility;in addition, the changes in the regime-switching phases are often related to the political mechanism design and the fundamental market factors. Those empirical results are beneficial for government decision-makers and market participants to strengthen risk management strategies, support emission-related investment decisions and optimize co-benefits of alternative energy-environmental policies. (C) 2017 Published by Elsevier B.V.

关键词： Emissions allowances China's emissions trading scheme Price dynamics Asymmetry effect GARCH model regime-switching process

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regime-switching measure of systemic financial stress

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ANNALS OF FINANCE 2013年第3期9卷 455-470页

作者： Abdymomunov, Azamat Fed Reserve Bank Richmond Charlotte Branch 530 East Trade St Charlotte NC 28223 USA

In this paper, I propose an approach to measuring systemic financial stress. In particular, abrupt and large changes in the volatility of financial variables that represent the dynamics of the US financial sector are modeled with a joint regime-switching process, distinguishing "low" and "high" volatility regimes. I find that the joint "high" volatility regime for the TED spread, return on the NYSE index, and capital-weighted CDS spread for large banks is closely related to periods of financial stress. This result suggests that the probability of the joint high volatility regime of these financial variables can be considered as a measure of systemic financial stress.

关键词： Financial stress Systemic risk regime-switching process SWARCH

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A trend-following strategy: Conditions for optimality

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AUTOMATICA 2011年第4期47卷 661-667页

作者： Kong, Hoi Tin Zhang, Qing Yin, G. George Univ Georgia Dept Math Athens GA 30602 USA Wayne State Univ Dept Math Detroit MI 48202 USA

Based on trend-following trading strategies that are widely used in the investment world, this work provides a set of sufficient conditions that determine the optimality of the traditional trend-following strategies when the trends are completely observable. A dynamic programming approach is used to verify the optimality under these conditions. The value functions are characterized by the associated HJB equations, and are shown to be either linear functions or infinity depending on the parameter values. The results reveal two counterintuitive facts: (a) trend following may not lead to optimal reward in some cases even when/if the investor knows exactly when a trend change occurs;(b) stock volatility is not relevant in trend following when trends are observable. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： regime-switching process Quasi-variational inequality Trend-following strategy

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Pricing swing options with regime switching

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ANNALS OF OPERATIONS RESEARCH 2011年第1期185卷 139-160页

作者： Wahab, M. I. M. Lee, Chi-Guhn Ryerson Univ Dept Mech & Ind Engn Toronto ON M5B 2K3 Canada Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada

Gasoline price is highly volatile and exhibits Markov regime-switching process. In the electricity and the natural gas markets, "swing" options, which can provide some protection against day-to-day price fluctuations, are used to incorporate flexibility in delivering acquired energy. We propose a framework for pricing swing options for an underlying variable that follows a regime-switching process. We study the proposed framework in the gasoline industry for pricing swing options under price uncertainty by extracting the gasoline market information, estimating the parameters of the regime-switching process, and then presenting different numerical examples.

关键词： Swing options regime-switching process Lattice approach

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Optimality Conditions for A Trend-Following Strategy

Optimality Conditions for A Trend-Following Strategy

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50th IEEE Conference of Decision and Control (CDC)/European Control Conference (ECC)

作者： Kong, Hoi Tin Zhang, Qing Yin, G. George Univ Georgia Dept Math Athens GA 30602 USA Univ Georgia Dept Math Boyd GSRC Athens GA 30602 USA Wayne State Univ Dept Math Detroit MI 48202 USA

ISBN: (纸本)9781612848013

Based on trend-following trading strategies that are widely used in the investment world, this work provides a set of sufficient conditions that determines the optimality of the traditional trend-following strategies when the trends are completely observable. A dynamic programming approach is used to verify the optimality under these conditions. The value functions are characterized by the associated HJB equations, and are shown to be either linear functions or infinity depending on the parameter values. The results reveal two counterintuitive facts: (a) trend following may not lead to optimal reward in some cases even when/if the investor knows exactly when a trend change occurs;(b) stock volatility is not relevant in trend following when trends are observable.

关键词： regime-switching process quasi-variational inequality trend-following strategy

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Optimality Conditions for A Trend-Following Strategy

Optimality Conditions for A Trend-Following Strategy

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IEEE Conference on Decision and Control

作者： Hoi Tin Kong Qing Zhang G. George Yin Department of Mathematics University of Georgia Athens GA 30602 Department of Mathematics Boyd GSRC The University of Georgia Athens GA 30602-7403 Department of Mathematics Wayne State University Detroit MI 48202

ISBN: (纸本)9781612848006

Based on trend-following trading strategies that are widely used in the investment world, this work provides a set of sufficient conditions that determines the optimality of the traditional trend-following strategies when the trends are completely observable. A dynamic programming approach is used to verify the optimality under these conditions. The value functions are characterized by the associated HJB equations, and are shown to be either linear functions or infinity depending on the parameter values. The results reveal two counter-intuitive facts: (a) trend following may not lead to optimal reward in some cases even when/if the investor knows exactly when a trend change occurs;(b) stock volatility is not relevant in trend following when trends are observable.

关键词： regime-switching process quasi-variational inequality trend-following strategy

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Pricing swing options in the electricity markets under regime-switching uncertainty

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QUANTITATIVE FINANCE 2010年第9期10卷 975-994页

作者： Wahab, M. I. M. Yin, Z. Edirisinghe, N. C. P. Univ Tennessee Dept Stat Operat & Management Sci Knoxville TN 37996 USA Ryerson Univ Dept Mech & Ind Engn Toronto ON M5B 2K3 Canada Univ Toronto Dept Mech & Ind Engn Toronto ON M5S 3G8 Canada

The spot price market for electricity is highly volatile. The time series of the daily average electricity price is characterised by seasonality, mean reversion, jumps, and regime-switching processes. In electricity markets, 'swing' contracts, which can provide some protection against the day-to-day price fluctuations, are used to incorporate flexibility in acquiring given quantities of electricity. We develop a lattice approach for the valuation of swing options by modelling the daily average price of electricity by a regime-switching process that utilises three regimes, consisting of Brownian motions and a mean-reverting process. Various numerical examples are presented to illustrate the methodology.

关键词： Swing option regime-switching process Mean-reverting process Electricity market

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