A Forward Monte Carlo Method for American Options Pricing

2012 ◽  
Vol 33 (4) ◽  
pp. 369-395 ◽  
Author(s):  
Daniel Wei-Chung Miao ◽  
Yung-Hsin Lee
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
American Options ◽  
Options Pricing

scholarly journals Using Logistic Regression of Machine Learning Method to Evaluate American Options

2021 ◽  
pp. 34-39
Author(s):  
Yung Hsin Lee
Keyword(s):  
Monte Carlo ◽  
Logistic Regression ◽  
Monte Carlo Method ◽  
Stock Price ◽  
American Options ◽  
Least Square Method ◽  
Classification Performance ◽  
Least Square ◽  
Strike Price ◽  
The Monte Carlo Method

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%.

A NEW MONTE CARLO METHOD FOR AMERICAN OPTIONS

2004 ◽  
Vol 07 (05) ◽  
pp. 591-614 ◽  
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.

scholarly journals A Multilevel Monte Carlo Method for the Valuation of Swing Options

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.

Analysis of Options Pricing Methods: the Black-Scholes Model and the Monte-Carlo Method

2020 ◽  
Vol 9 (3) ◽  
pp. 39-42
Author(s):  
Leysen Yunusova
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Investment Decisions ◽  
Estimation Methods ◽  
Options Pricing ◽  
Financial Instruments ◽  
Strategic Investment ◽  
Black Scholes Model ◽  
The Monte Carlo Method ◽  
Black Scholes

Currently, the market of financial instruments is quite developed. Traditional financial instruments prevail on the Russian market, while derivatives of these financial instruments (options, futures, forwards, bills, etc.) are faintly developed. The reason for this situation is that few participants in the financial market can correctly evaluate financial products. Scientific researchers and large companies use different methods of estimating the value of financial instruments in making strategic investment decisions, since incorrect calculations can be irreparable. Therefore, it is important to apply the appropriate pricing methodology to various derivative financial instruments. The topic of derivative financial instruments in terms of scientific and theoretical aspects has been worked out in sufficient volume, but as for the pricing of these instruments, there are some gaps. There is still no method for pricing derivatives that would allow you to accurately assess the value of financial instruments for subsequent effective investment decisions. In this article considers the methodology of pricing of derivative financial instruments using the Black-Scholes model and the Monte Carlo method. The presented estimation methods allow us to calculate the range of price values that allows us to provide the most accurate expected results.

scholarly journals Avaliação de Opções Americanas com Barreiras Monitoradas de Forma Discreta

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.

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

1974 ◽  
Vol 22 ◽  
pp. 307 ◽  
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.

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

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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