A new tree method for pricing financial derivatives in a regime-switching mean-reverting model

Liu, R.H.

doi:10.1016/j.nonrwa.2012.03.006

Cited by 25 publications

(13 citation statements)

References 39 publications

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“…We now show the tree construction, which is initially designed by Liu [32]. For the node with ( , ) = ( , ), we consider how it evolves in the next time.…”

Section: Valuation Of Swing Options In Trinomial Forestmentioning

confidence: 99%

“…Hence, there are three branches emanating from = . Besides, Liu [32] designed three structures of the branches, and in different structures +1 , +1 , and +1 are also different. Choosing which structure depends on the comparison result between and the two threshold values ,1 and ,2 as follows:…”

Section: Valuation Of Swing Options In Trinomial Forestmentioning

confidence: 99%

“…It is emphasized that ,1 and ,2 change with the state of regime . More details on this mechanism of the tree designing can be found in [32].…”

Section: Valuation Of Swing Options In Trinomial Forestmentioning

confidence: 99%

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Valuation of Swing Options under a Regime‐Switching Mean‐Reverting Model

Shao

Xiang

2019

Mathematical Problems in Engineering

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In this paper, we study the valuation of swing options on electricity in a model where the underlying spot price is set to be the product of a deterministic seasonal pattern and Ornstein-Uhlenbeck process with Markov-modulated parameters. Under this setting, the difficulties of pricing swing options come from the various constraints embedded in contracts, e.g., the total number of rights constraint, the refraction time constraint, the local volume constraint, and the global volume constraint. Here we propose a framework for the valuation of the swing option on the condition that all the above constraints are nontrivial. To be specific, we formulate the pricing problem as an optimal stochastic control problem, which can be solved by the trinomial forest dynamic programming approach. Besides, empirical analysis is carried out on the model. We collect historical data in Nord Pool electricity market, extract the seasonal pattern, calibrate the Ornstein-Uhlenbeck process parameters in each regime, and also get market price of risk. Finally, on the basis of calibration results, a specific numerical example concerning all typical constraints is presented to demonstrate the valuation procedure.

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“…We now show the tree construction, which is initially designed by Liu [32]. For the node with ( , ) = ( , ), we consider how it evolves in the next time.…”

Section: Valuation Of Swing Options In Trinomial Forestmentioning

confidence: 99%

Section: Valuation Of Swing Options In Trinomial Forestmentioning

confidence: 99%

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Valuation of Swing Options under a Regime‐Switching Mean‐Reverting Model

Shao

Xiang

2019

Mathematical Problems in Engineering

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“…Markov regime switching models were first introduced by Hamilton [1] and recently have become popular in financial applications including equity options [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17], bond prices and interest rate derivatives [18][19][20], portfolio selection [21], and trading rules [22][23][24][25][26]. The Markov regime switching models allow the model parameters (drift and volatility coefficients) to depend on a Markov chain which can reflect the information of the market environments and at the same time preserve the simplicity of the models.…”

Section: Introductionmentioning

confidence: 99%

Laplace Transform Methods for a Free Boundary Problem of Time-Fractional Partial Differential Equation System

Zhou

Gao

2017

Discrete Dynamics in Nature and Society

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We study the pricing of the American options with fractal transmission system under two-state regime switching models. This pricing problem can be formulated as a free boundary problem of time-fractional partial differential equation (FPDE) system. Firstly, applying Laplace transform to the governing FPDEs with respect to the time variable results in second-order ordinary differential equations (ODEs) with two free boundaries. Then, the solutions of ODEs are expressed in an explicit form. Consequently the early exercise boundaries and the values for the American option are recovered using the Gaver-Stehfest formula. Numerical comparisons of the methods with the finite difference methods are carried out to verify the efficiency of the methods.

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“…Liu [25] extended the idea of [7] and developed a linear tree for the switching model with m ≥ 2 regimes. Liu [26] further extended the tree method to a class of regime-switching mean-reverting models. Yuen and Yang [38] modified the trinomial tree of [8] to construct a fast and simple tree method for pricing both vanilla and exotic options in a Markovian regime-switching model.…”

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confidence: 99%

A tree approach to options pricing under regime-switching jump diffusion models

Liu

Nguyen

2015

International Journal of Computer Mathematics

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A simple, efficient tree is developed to price options in a very general regime switching jump diffusion model. Under this model, the switching rates of the switching process depend on the underlying stock price process. Sufficient conditions that guarantee the positivity of branch probabilities are provided. Using the regime switching tree, we approximate Heston's stochastic volatility model with an additional jump component. Finally, we illustrate the effectiveness of the tree method by several numerical examples.

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A new tree method for pricing financial derivatives in a regime-switching mean-reverting model

Cited by 25 publications

References 39 publications

Valuation of Swing Options under a Regime‐Switching Mean‐Reverting Model

Valuation of Swing Options under a Regime‐Switching Mean‐Reverting Model

Laplace Transform Methods for a Free Boundary Problem of Time-Fractional Partial Differential Equation System

A tree approach to options pricing under regime-switching jump diffusion models

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