Stock Liquidation via Stochastic Approximation Using Nasdaq Daily and Intra‐day Data

Yin, George; Zhang, Q.; Liu, F.; Liu, R. H.; Cheng, Yu‐Shan

doi:10.1111/j.1467-9965.2006.00269.x

Cited by 21 publications

(16 citation statements)

References 12 publications

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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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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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“…They are not the most general ones available. Weaker conditions on the regularity are possible (see [15]). However, here our main objective is to present the functional dependence of the error estimates on bias, noise, and stepsize.…”

Section: Algorithms For Pricing American Put Options At Any Given Timementioning

confidence: 99%

“…Concerning exponential type utility functions, convergence and rates of convergence of algorithms (4) and (5) were studied in [14]. Further large deviations type results were obtained in [15].…”

mentioning

confidence: 99%

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Using stochastic optimization methods for stock selling decision making and option pricing: numerics and bias and variance dependent convergence rates

Bao¹,

Belu²,

Gershon³

et al. 2007

Communications in Information and Systems

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Abstract. This paper is concerned with using stochastic approximation and optimization methods for stock liquidation decision making and option pricing. For stock liquidation problem, we present a class of stochastic recursive algorithms, and make comparisons of performances using stochastic approximation methods and that of certain commonly used heuristic methods, such as moving averaging method and moving maximum method. Stocks listed in NASDAQ are used for making the comparisons. For option pricing, we design stochastic optimization algorithms and present numerical experiments using data derived from Berkeley Options Data Base. An important problem in these studies concerns the rate of convergence taking into consideration of bias and noise variance. In an effort to ascertain the convergence rates incorporating the computational efforts, we use a Liapunov function approach to obtain the desired convergence rates. Variants of the algorithms are also suggested.

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“…We point out that the method can be extended to treat the case that the precise model is not available; see [15] for demonstrations using NASDAQ market data. Recently, Helmes [6] considered computational issues of the selling rule using a linear programming approach.…”

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confidence: 99%

Selling a large stock position: a stochastic control approach with state constraints

Pemy¹,

Zhang²,

Yin³

2007

Communications in Information and Systems

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Abstract. A common practice for stock-selling decision making is often concerned with liquidation of the security in a short duration. This is feasible when a relative smaller number of shares of a stock is treated. Selling a large position during a short period of time in the market frequently depresses the market, resulting in poor filling prices. In this work, liquidation strategies are considered for selling much smaller number of shares over a longer period of time. By using a fluid model in which the number of shares are treated as fluid, and the corresponding liquidation is dictated by the rate of selling over time. Our objective is to maximize the expected overall return. The problem is formulated as a stochastic control problem with state constraints. Using the method of constrained viscosity solutions, we characterize the dynamics governing the value function and the associated boundary conditions. Numerical algorithms are also provided along with an illustrative example for demonstration purposes.

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Stock Liquidation via Stochastic Approximation Using Nasdaq Daily and Intra‐day Data

Cited by 21 publications

References 12 publications

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

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

Using stochastic optimization methods for stock selling decision making and option pricing: numerics and bias and variance dependent convergence rates

Selling a large stock position: a stochastic control approach with state constraints

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