Monte Carlo Simulation for American Options

Caflisch, Russel E.; Chaudhary, Suneal K.

doi:10.1007/978-94-017-0427-4_1

Cited by 4 publications

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References 28 publications

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“…In [5,8,9], we developed an accelerated numerical method for evaluation of American options. This method is based on the Least Squares Method (LSM) of Longstaff and Schwartz, which used Monte Carlo simulation of the price of the underlying security, combined with a least square regression to perform the projected values that are required in making early exercise decisions.…”

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Analytic and Numerical Methods for Epitaxial Growth and Computer Aided Design

Caflisch¹

2006

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Under support from this grant, we performed work on simulation and design for a number of important topics. These included level set modeling of dendritic solidification, regularized Wulff flows, singularities for flow in porous media, evaluation of American options, epitaxial growth and strain, and electrodeposition. Key results include the following:In [1], we developed a new reduced order model for epitaxial growth. The the average coverage, the average island size and the average inter-island distance at each layer of the system. The resulting equations are a system of 3n ODEs for a epitaxial film of thickness n layers. This system displays good agreement with the oscillations observed in RHEED measurements during MBE growth, including the variations in the envelope of the oscillations. We expect this model to be useful both for basic understanding and as a tool for control methods.In [2], we presented a level set approach for the modeling of dendritic solidification. These simulations used a new second order accurate symmetric discretization of the Poisson equation. Numerical results indicated that this method can be used successfully on complex interfacial shapes and can simulate many of the physical features of dendritic solidification. We applied this algorithm to the simulation of the dendritic crystallization of a pure melt and find that the dendrite tip velocity and tip shapes are in excellent agreement with solvability theory. Numerical results were presented in both two and three spatial dimensions.In [3], we proposed a method of regularizing the backwards parabolic partial differential equations that arise from using gradient descent to minimize surface energy integrals within a level set framework in 2 and 3 dimensions. The proposed regularization energy is a functional of the mean curvature of the surface. Our method used a local level set technique to evolve the resulting fourth order PDEs in time. Numerical results are shown, indicating for the first time, stability and convergence to the asymptotic Wulff shape.In [4], we analyze the Muskat problem that describes the motion of two fluids of different viscosities in a porous material. This problem is linearly stable if the less viscous fluid is moving into the more viscous fluid and linearly unstable in the reverse case. We find that the linearly unstable problem is ill-posed and can develop singularities on the interface between the two fluids. In addition for linearly stable configuration, we show that there is global existence for initial

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Analytic and Numerical Methods for Epitaxial Growth and Computer Aided Design

Caflisch¹

2006

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Quasi‐MonteCarlo Methods

Niederreiter¹

2010

Encyclopedia of Quantitative Finance

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This article presents a survey of quasi‐Monte Carlo methods for multidimensional numerical integration and their applications to computational finance. Quasi‐Monte Carlo methods are deterministic versions of Monte Carlo methods, which outperform Monte Carlo methods for many types of integrals. First, a general background on quasi‐Monte Carlo methods is given. Then we describe principles for the construction of low‐discrepancy sequences, which are basic ingredients of any implementation of quasi‐Monte Carlo methods. Special emphasis is placed on the currently most powerful constructions based on the digital method and the theory of ( T , s )‐sequences. Next, the important concept of effective dimension is discussed. One section is devoted to scrambling schemes for low‐discrepancy sequences. A review of applications to pricing problems, in particular for mortgage‐backed securities and options, concludes the article.

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Low-Discrepancy Simulation

Niederreiter

2011

Handbook of Computational Finance

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Monte Carlo Simulation for American Options

Cited by 4 publications

References 28 publications

Analytic and Numerical Methods for Epitaxial Growth and Computer Aided Design

Analytic and Numerical Methods for Epitaxial Growth and Computer Aided Design

Quasi‐MonteCarlo Methods

Low-Discrepancy Simulation

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