Calibrating weighted Monte-Carlo method to American options

Aims: The main purpose of this study is to understand whether Logistic regression has certain benefits in the evaluation of American options. As far as the Monte Carlo method is concerned, the least square method is traditionally used to evaluate American options, but in fact, Logistic regression is generally quite good in classification performance. Therefore, this study wants to know if Logistic regression can improve the accuracy of evaluation in American options. Study Design: The selection of options parameters required in the simulation process mainly considers the average level of actual market conditions in the past few years in terms of dividend yield and risk-free interest rate. The part of the stock price and the strike price mainly considers three different situations: in-the-money, out-of-the-money and at the money. Methodology: This study applied the Logistic regression in Monte Carlo method for the pricing of American. Uses the ability of logistic regression to help determine whether the American option should be exercised early for each stock price path. The validity of the proposed method is supported by some vanilla put cases testing. The parameters used in all cases tested are considered the current state of the market. Conclusion: This study demonstrates the effectiveness of the proposed approach using numerical examples, revealing signiﬁcant improvements in numerical efﬁciency and accuracy. Several test cases showed that the relative error of all tests are below 1%.

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A NEW MONTE CARLO METHOD FOR AMERICAN OPTIONS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024904002554 ◽

2004 ◽

Vol 07 (05) ◽

pp. 591-614 ◽

Cited By ~ 6

Author(s):

G. N. MILSTEIN ◽

O. REIß ◽

J. SCHOENMAKERS

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Monte Carlo Method ◽

Boundary Value Problem ◽

Numerical Experiments ◽

American Options ◽

American Option ◽

Parabolic Boundary ◽

Black Scholes ◽

Exercise Boundary

We introduce a new Monte Carlo method for constructing the exercise boundary of an American option in a generalized Black–Scholes framework. Based on a known exercise boundary, it is shown how to price and hedge the American option by Monte Carlo simulation of suitable probabilistic representations in connection with the respective parabolic boundary value problem. The method presented is supported by numerical experiments.

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A Multilevel Monte Carlo Method for the Valuation of Swing Options

Mathematical Problems in Engineering ◽

10.1155/2021/8407324 ◽

2021 ◽

Vol 2021 ◽

pp. 1-7

Author(s):

Hakimeh Ghodssi-Ghassemabadi ◽

Gholam Hossein Yari

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

American Options ◽

Numerical Results ◽

Multilevel Monte Carlo ◽

Swing Options ◽

Novel Approach ◽

Black Scholes ◽

Price Estimation ◽

Multilevel Monte Carlo Method

In this study, we propose a novel approach for the valuation of swing options. Swing options are a kind of American options with multiple exercise rights traded in energy markets. Longstaff and Schwartz have suggested a regression-based Monte Carlo method known as the least-squares Monte Carlo (LSMC) method to value American options. In this work, first we introduce the LSMC method for the pricing of swing options. Then, to achieve a desired accuracy for the price estimation, we combine the idea of LSMC with multilevel Monte Carlo (MLMC) method. Finally, to illustrate the proper behavior of this combination, we conduct numerical results based on the Black–Scholes model. Numerical results illustrate the efficiency of the proposed approach.

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Avaliação de Opções Americanas com Barreiras Monitoradas de Forma Discreta

Brazilian Review of Finance ◽

10.12660/rbfin.v7n4.2009.1398 ◽

2009 ◽

Vol 7 (4) ◽

pp. 503

Author(s):

Giuliano Carroza Uzêda Iorio de Souza ◽

Carlos Patrício Samanez

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

American Options ◽

Adaptive Mesh ◽

Bisection Method ◽

Quasi Monte Carlo ◽

Mesh Model ◽

Definition Of

This article presents an approach and a model to valuing discrete barrier American options. The developed model consists of an adaptation of the method of Grant, Vora and Weeks (1997), in order to allow to incorporate the barriers. The Hybrid Quasi-Monte Carlo method was used in the simulations and the Bisection method in the definition of the options trigger curves. The results found in the application of the developed model were compared with the estimated by the Adaptive Mesh Model, developed by Ahn et al (1999). In addition, the sensitivity of the options price relative to changes in inputs parameters was analyzed, confirming the consistence of the model.

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Outbursts of comet Schwassmann-Wachmann 1, and the cloud of interplanetary boulders

International Astronomical Union Colloquium ◽

10.1017/s0252921100034035 ◽

1974 ◽

Vol 22 ◽

pp. 307 ◽

Cited By ~ 3

Author(s):

Zdenek Sekanina

Keyword(s):

Monte Carlo ◽

Monte Carlo Method ◽

Interplanetary Space ◽

Porous Matrix ◽

Maximum Diameter ◽

Expansion Velocity ◽

Solid Constituent ◽

Meteoric Material ◽

Periodic Comet

AbstractIt is suggested that the outbursts of Periodic Comet Schwassmann-Wachmann 1 are triggered by impacts of interplanetary boulders on the surface of the comet’s nucleus. The existence of a cloud of such boulders in interplanetary space was predicted by Harwit (1967). We have used the hypothesis to calculate the characteristics of the outbursts – such as their mean rate, optically important dimensions of ejected debris, expansion velocity of the ejecta, maximum diameter of the expanding cloud before it fades out, and the magnitude of the accompanying orbital impulse – and found them reasonably consistent with observations, if the solid constituent of the comet is assumed in the form of a porous matrix of lowstrength meteoric material. A Monte Carlo method was applied to simulate the distributions of impacts, their directions and impact velocities.

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Structures and crystallization of vacuum-deposited amorphous Se and Sb films

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100173832 ◽

1990 ◽

Vol 48 (4) ◽

pp. 140-141

Author(s):

Makoto Shiojiri ◽

Toshiyuki Isshiki ◽

Tetsuya Fudaba ◽

Yoshihiro Hirota

Keyword(s):

Monte Carlo ◽

Electron Microscope ◽

Monte Carlo Method ◽

Computer Program ◽

Radial Distribution ◽

Film Formation ◽

Amorphous State ◽

Two Dimensional ◽

Amorphous Films ◽

Binding Condition

In hexagonal Se crystal each atom is covalently bound to two others to form an endless spiral chain, and in Sb crystal each atom to three others to form an extended puckered sheet. Such chains and sheets may be regarded as one- and two- dimensional molecules, respectively. In this paper we investigate the structures in amorphous state of these elements and the crystallization.HRTEM and ED images of vacuum-deposited amorphous Se and Sb films were taken with a JEM-200CX electron microscope (Cs=1.2 mm). The structure models of amorphous films were constructed on a computer by Monte Carlo method. Generated atoms were subsequently deposited on a space of 2 nm×2 nm as they fulfiled the binding condition, to form a film 5 nm thick (Fig. 1a-1c). An improvement on a previous computer program has been made as to realize the actual film formation. Radial distribution fuction (RDF) curves, ED intensities and HRTEM images for the constructed structure models were calculated, and compared with the observed ones.

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