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American Put Option Pricing Using A Hybrid Evolutionary Computation And Monte Carlo Simulation Method
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Book Synopsis American Put Option Pricing Using a Hybrid Evolutionary Computation and Monte-Carlo Simulation Method by : Anjan Kumar Swain
Download or read book American Put Option Pricing Using a Hybrid Evolutionary Computation and Monte-Carlo Simulation Method written by Anjan Kumar Swain and published by . This book was released on 2017 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: American put option pricing is a challenging, complex problem, and existing methods to address this problem are computationally intensive. In this paper, a self-adaptive evolutionary computation method is used for computing American put option price. The proposed method essentially transforms a discrete time exercisable American option to a continuous time exercisable option. The performance of the proposed method is compared with that of plain European Monte Carlo and Binomial Lattice option values. Further, in pricing American options this method exhibited better results with considerable improvements over that of conventional Monte-Carlo simulation method. It is argued that the proposed method effectively computes the upper bound on the American put options.
Book Synopsis Monte Carlo Methods for American Option Pricing by : Alberto Barola
Download or read book Monte Carlo Methods for American Option Pricing written by Alberto Barola and published by LAP Lambert Academic Publishing. This book was released on 2014-05-21 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Monte Carlo approach has proved to be a valuable and flexible computational tool in modern finance. A number of Monte Carlo simulation-based methods have been developed within the past years to address the American option pricing problem. The aim of this book is to present and analyze three famous simulation algorithms for pricing American style derivatives: the stochastic tree; the stochastic mesh and the least squares method (LSM). The author first presents the mathematical descriptions underlying these numerical methods. Then the selected algorithms are tested on a common set of problems in order to assess the strengths and weaknesses of each approach as a function of the problem characteristics. The results are compared and discussed on the basis of estimates precision and computation time. Overall the simulation framework seems to work considerably well in valuing American style derivative securities. When multi-dimensional problems are considered, simulation based methods seem to be the best solution to estimate prices since the general numerical procedures of finite difference and binomial trees become impractical in these specific situations.
Book Synopsis Pricing American Options Using Monte Carlo Simulation by : Victoria Zhanna Averbukh
Download or read book Pricing American Options Using Monte Carlo Simulation written by Victoria Zhanna Averbukh and published by . This book was released on 1997 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Enhanced Monte Carlo Estimates for American Option Prices by : Mark Broadie
Download or read book Enhanced Monte Carlo Estimates for American Option Prices written by Mark Broadie and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo simulation has trouble with American options because the exercise decision at a given date must compare the option's immediate exercise value against its continuation value. The option value if it is not exercised is a function of its value along all possible future price paths from that point on, and each path will present further exercise decisions with the same difficulty in resolving them. The authors propose a hybrid valuation technique that bridges Monte Carlo simulation and lattice methods. Instead of simulating price paths, they simulate whole price trees. The tree emanating from each point is used to assess the option continuation value for that date and stock price. While the results are accurate, inevitably the procedure requires a large number of computations. The authors then offer a variety of techniques that substantially increase efficiency.
Book Synopsis Valuation of American Options by : David Animante
Download or read book Valuation of American Options written by David Animante and published by . This book was released on 2016 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of American style equity options as hedging instrument has gained currency in recent times. This phenomenon devolves from the ever-expanding need by individuals, corporations and governments to hedge away their financial risks and the clarion call for derivative securities that give the holder increased flexibility in exercise. Nevertheless, pricing American options is complex and there exists no analytic solution to the problem except a profusion of approximation and finite difference techniques. Indeed, many researchers have shown that these methods cannot handle multifactor situations where the underlying asset follows a jump-diffusion process and where the derivative security depends on multiple sources of uncertainty such as stochastic volatility, stochastic interest rate among others. Monte-Carlo simulation techniques therefore developed out of the search for a pricing formula that has the capacity to accommodate all forms of uncertainty and at the same time able to produce speedy and accurate results. Some scholars at first rejected these techniques as yielding inaccurate results but in recent times, many researchers have demonstrated the efficacy of Monte-Carlo simulation in option pricing. The aim of this study is to assess the effectiveness of Monte-Carlo simulation methods in comparison with other option pricing techniques. To achieve this objective, the research builds an algorithm to compute Call and Put prices based on a wide range of input parameters. It also develops a model where volatility or interest rate is stochastic and a deterministic function of time. The results indicate that Monte-Carlo simulation techniques produce option values and exercise boundaries that are very similar to the Binomial, Barone-Adesi and Whaley as well as the Explicit Finite Difference methods. The results also show that the stochastic volatility and stochastic interest rate models yield slightly different but more accurate results. Consequently, the study recommends simulation techniques that incorporate multiple sources of uncertainty simultaneously for fast, efficient and more accurate option pricing.
Book Synopsis A Monte Carlo Method for Pricing American Options by : Diego Garcia
Download or read book A Monte Carlo Method for Pricing American Options written by Diego Garcia and published by . This book was released on 1999 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing Using Monte Carlo Methods by : Mengliu Lu
Download or read book Option Pricing Using Monte Carlo Methods written by Mengliu Lu and published by . This book was released on 2011 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: This paper aims to use Monte Carlo methods to price American call options on equities using the variance reduction technique of control variates and to price American put options using the binomial model. We use this information to form option positions. This project was done a part of the masters capstone course Math 573: Computational Methods of Financial Mathematics.
Book Synopsis An Adaptive Evolutionary Approach to Option Pricing Via Genetic Programming by : N.K. Chidambaran
Download or read book An Adaptive Evolutionary Approach to Option Pricing Via Genetic Programming written by N.K. Chidambaran and published by . This book was released on 2010 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a methodology of Genetic Programming to approximate the relationship between the option price, its contract terms and the properties of the underlying stock price. An important advantage of the Genetic Programming approach is that we can incorporate currently known formulas, such as the Black-Scholes model, in the search for the best approximation to the true pricing formula. Using Monte Carlo simulations, we show that the Genetic Programming model approximates the true solution better than the Black-Scholes model when stock prices folow a jump-diffusion process. We also show that the Genetic Programming model outperforms various other models in many different settings. Other advantages of the Genetic Programming approach include its robustness to changing environment, its low demand for data, and its computational speed. Since genetic programs are flexible, self-learning and sefl-improving, they are an ideal tool for practitioners.
Book Synopsis Option Pricing Using Monte Carlo Methods by : Junxiong Wang
Download or read book Option Pricing Using Monte Carlo Methods written by Junxiong Wang and published by . This book was released on 2011 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: This project is devoted primarily to the use of Monte Carlo methods to simulate stock prices in order to price European call options using control variates, and to the use of the binominal model to price American put options. At the end, we can use the information to form a portfolio position using an Interactive Brokers paper trading account. This project was done as a part of the masters capstone course Math 573: Computational Methods of Financial Mathematics.
Book Synopsis Pricing American Options by : Leonid Kogan
Download or read book Pricing American Options written by Leonid Kogan and published by . This book was released on 2001 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a new method for pricing American options. The main practical contribution of this paper is a general algorithm for constructing upper and lower bounds on the true price of the option using any approximation to the option price. We show that our bounds are tight, so that if the initial approximation is close to the true price of the option, the bounds are also guaranteed to be close. We also explicitly characterize the worst-case performance of the pricing bounds. The computation of the lower bound is straightforward and relies on simulating the suboptimal exercise strategy implied by the approximate option price. The upper bound is also computed using Monte Carlo simulation. This is made feasible by the representation of the American option price as a solution of a properly defined dual minimization problem, which is the main theoretical result of this paper. Our algorithm proves to be accurate on a set of sample problems where we price call options on the maximum and the geometric mean of a collection of stocks. These numerical results suggest that our pricing method can be successfully applied to problems of practical interest. Keywords: Asset pricing, dynamic programming, simulation, American option, optimal stopping, duality.
Book Synopsis Mathematical Modeling And Methods Of Option Pricing by : Lishang Jiang
Download or read book Mathematical Modeling And Methods Of Option Pricing written by Lishang Jiang and published by World Scientific Publishing Company. This book was released on 2005-07-18 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black-Scholes-Merton's option pricing theory.A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.
Book Synopsis Monte Carlo Simulation with Machine Learning for Pricing American Options and Convertible Bonds by : Bella Dubrov
Download or read book Monte Carlo Simulation with Machine Learning for Pricing American Options and Convertible Bonds written by Bella Dubrov and published by . This book was released on 2015 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Li, Szepesvari and Schuurmans (2009) show that reinforcement learning (RL) algorithms are superior to the classical methods (such as Longstaff and Schwartz (2001)) in pricing American options using Monte Carlo simulation. We extend their techniques to the problem of pricing convertible bonds and show that RL outperforms LS on this task. Additionally, we propose a new method, based on the random forest algorithm from machine learning [Breiman (2001)], that can be used for pricing both American options and convertible bonds with Monte Carlo simulation. We show that this algorithm outperforms LS and is also superior to RL in most cases. We demonstrate how to use Monte Carlo simulation with the methods described above for pricing a complex convertible bond trading at the Tel Aviv stock exchange. Like many Israeli convertibles, this bond exhibits the "gradually diminishing principal" feature, meaning that instead of one payment of the principal at maturity, there are multiple principal payments during the lifetime of the bond. This feature presents a challenge to existing models. We also model other exotic features of this bond, such as path-dependent conversion ratio and exchange rate indexation. The prices that we obtain using this model are close to the market prices of the bond.
Book Synopsis Use of the Monte Carlo Simulation in Valuation of European and American Call Options by : Gorica Malesevic
Download or read book Use of the Monte Carlo Simulation in Valuation of European and American Call Options written by Gorica Malesevic and published by . This book was released on 2017 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis examines the valuation methods used for pricing European and American call options. Options are financial instruments that play an important role in the financial industry and are used in hedging, speculating and arbitraging. Because options are widely used in investing, there is a need for valuation methods that are as precise as possible. Options have been perceived as obscure financial instruments due to the lack of valuation techniques in the past. However, with the discovery of Black-Scholes Model in 1973, the first option valuation method, option trading escalated. In this thesis, the fair market value of S & P 500 index with European exercise style, The Google Option Contract and Apple Option Contract will be obtained bu using the Black-Scholes Model, the General Monte Carlo Simulation, The Combined Method and the Least-Square Monte Carlo. The results from three models with be compared and contrasted in order to determine the best valuation method.
Book Synopsis Computational Methods for Option Pricing by : Bingxin Fei
Download or read book Computational Methods for Option Pricing written by Bingxin Fei and published by . This book was released on 2011 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: This paper aims to practice the use of Monte Carlo methods to simulate stock prices in order to price European call options using control variates. American put options are priced using the binomial model separately. Finally, we use the information to form a portfolio position using an Interactive Brokers paper trading account.
Book Synopsis The Hyperbolic Model: Option Pricing Using Approximation and Quasi-Monte Carlo Methods by : Martin Predota
Download or read book The Hyperbolic Model: Option Pricing Using Approximation and Quasi-Monte Carlo Methods written by Martin Predota and published by GRIN Verlag. This book was released on 2009-04 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doctoral Thesis / Dissertation from the year 2002 in the subject Mathematics - Stochastics, grade: 1, Technical University of Graz, language: English, abstract: Aus Sicht der Mathematik spielen Optionen eine wesentliche Rolle seit der bahnbrechenden Arbeit von Black und Scholes im Jahre 1973. Deren Modell basiert jedoch auf der unrealistischen Annahme, das log-returns von Aktienkursen normalverteilt sind. Eberlein und Keller haben 1995 gezeigt, daß solche log-returns hyperbolisch verteilt sind. Die vorliegende Arbeit baut auf dieser Annahme auf und erweitert das Optionsspektrum von Europäischen Optionen auf Asiatische, Amerikanische sowie Multi-Asset-Optionen. Weiters wird das "Standard"-Martingal-Maß, die sogenannte Esscher-Transformation, durch das Entropie-minimierende Maß erweitert. Da jedoch keine exakte Preissetzung solcher Optionen möglich ist, wird auf numerische Simulationen und Approximationen zurückgegriffen. Die verwendeten numerischen Verfahren sind die Monte Carlo-Methode mit verschiedenen Varianzreduktionstechniken und die Quasi-Monte Carlo Methode.
Book Synopsis Mathematical Modeling and Methods of Option Pricing by : Lishang Jiang
Download or read book Mathematical Modeling and Methods of Option Pricing written by Lishang Jiang and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.
Book Synopsis American-Asian Option Pricing Based on Monte Carlo Simulation Method by : Shiguang Han
Download or read book American-Asian Option Pricing Based on Monte Carlo Simulation Method written by Shiguang Han and published by . This book was released on 2012 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:
