Download or read book Computing the Optimal Early Exercise Boundary and the Premium for American Put Options written by Sze Ki Tang and published by . This book was released on 2010 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Calculating the Optimal Exercise Boundary of American Put Options with an Approximation Formula written by Song-Ping Zhu and published by . This book was released on 2005 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book American Put Options written by Donna Salopek and published by CRC Press. This book was released on 1997-03-15 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: An American put option gives its owner the right to sell a share of stock at a given specified price on or before a given date. This book provides a detailed comparison of recent works on the American put option from both theoretical and computational approaches.
Download or read book Hints for an Extension of the Early Exercise Premium Formula for American Options written by Hans-Peter Bermin and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The characterization of the American put option price is still an open issue. From the beginning of the nineties there exists a non-closed formula for this price but nontrivial numerical computations are required to solve it. Strong efforts have been made to propose computational efficient methods but few of them have strong mathematical reasoning to ascertain why these methods work well and how important it is to consider a good approximation to the boundary or to the smooth pasting condition. We present an extension of the American put price aiming to catch weaknesses of the numerical methods given in the literature.
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.
Download or read book The American Put and European Options Near Expiry Under Levy Processes written by Sergei Levendorskii and published by . This book was released on 2004 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive explicit formulas for time decay, for the European call and put options at expiry, and use them to calculate analytical approximations to the price of the American put and early exercise boundary near expiry. We show that for many families of non-Gaussian processes used in empirical studies of financial markets, the early exercise boundary for the American put without dividends is separated from the strike price by a non-vanishing margin on the time interval up to expiry, the expiry date excluding. As the riskless rate vanishes and the drift decreases accordingly so that the stock remains a martingale, the optimal exercise price goes to zero uniformly over the time interval up to expiry, the expiry date excluding. The implications for parameters' fitting are discussed.
Download or read book The Early Exercise Premium in American Put Option Prices written by Malin Engstrom and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This study estimates the value of the early exercise premium in American put option prices using Swedish equity options data. The value of the premium is found as the deviation of the American put price from European put-call parity, and in addition a theoretical estimate of the premium is computed. The empirically found premium is also used in a modified version of the control variate approach to value American puts. The results indicate a substantial value of the early exercise premium, where the premium derived from put-call parity is higher than the theoretical premium. The premium also increases with moneyness and time left to expiration, while the effect of interest rate and volatility depends on the moneyness of the option. The modified control variate technique works reasonably well relative the theoretical models. In particular, for deep in-the-money options, this technique is superior.
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.
Download or read book Optimal Exercise Boundary in a Binomial Option Pricing Model written by In Joon Kim and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Previous studies pointed out that the determination of the optimal exercise boundary is an important element in the valuation of American options. A correct understanding of the behavior of the optimal exercise boundary is crucial for the valuation of American options. In this paper, the properties associated with the optimal exercise boundary in a binomial option pricing model are examined and an efficient recursive valuation method which incorporates these properties is presented. This valuation method represents a substantial improvement over the conventional binomial model in terms of computational efficiency with exactly the same accuracy.
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:
Download or read book Options Markets written by John C. Cox and published by Prentice Hall. This book was released on 1985 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes the first published detailed description of option exchange operations, the first published treatment using only elementary mathematics and the first step-by-step procedure for implementing the Black-Scholes formula in actual trading.
Download or read book Approximating the Optimal Exercise Boundary for American Options via Least Squares Monte Carlo written by Qiang Liu and published by . This book was released on 2015 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: The least-squares Monte Carlo method of Longstaff-Schwartz is utilized to construct the optimal exercise boundary (OXB) of an American put option when the underlying follows a geometric Brownian motion (GBM). The optimal exercise price at each time step is obtained by solving numerically the equation of the exercising boundary condition. The set of such exercise prices, along with their ldquo;standard deviations,rdquo; is then fitted to a smooth, monotonic model of a sum of three exponential functions to approximate the OXB, which turns out to be very close to the exact solution of the boundary. The approach can be efficiently implemented and readily computed in practice, and should be applicable to cases when the underlying price process is not GBM.
Download or read book Applied Computational Economics and Finance written by Mario J. Miranda and published by MIT Press. This book was released on 2004-08-20 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a variety of computational methods used to solve dynamic problems in economics and finance. It emphasizes practical numerical methods rather than mathematical proofs and focuses on techniques that apply directly to economic analyses. The examples are drawn from a wide range of subspecialties of economics and finance, with particular emphasis on problems in agricultural and resource economics, macroeconomics, and finance. The book also provides an extensive Web-site library of computer utilities and demonstration programs. The book is divided into two parts. The first part develops basic numerical methods, including linear and nonlinear equation methods, complementarity methods, finite-dimensional optimization, numerical integration and differentiation, and function approximation. The second part presents methods for solving dynamic stochastic models in economics and finance, including dynamic programming, rational expectations, and arbitrage pricing models in discrete and continuous time. The book uses MATLAB to illustrate the algorithms and includes a utilities toolbox to help readers develop their own computational economics applications.
Download or read book American Style Derivatives written by Jerome Detemple and published by CRC Press. This book was released on 2005-12-09 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on recent developments in the field, American-Style Derivatives provides an extensive treatment of option pricing with emphasis on the valuation of American options on dividend-paying assets. This book reviews valuation principles for European contingent claims and extends the analysis to American contingent claims. It presents basic valuation principles for American options including barrier, capped, and multi-asset options. It also reviews numerical methods for option pricing and compares their relative performance. Ideal for students and researchers in quantitative finance, this material is accessible to those with a background in stochastic processes or derivative securities.
Download or read book Probabilities and Values of Early Exercise written by James N. Bodurtha and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This article analyzes fundamental differences between American spot and futures options. These options differ in their early exercise probabilities and values, and in option buyers' exercise behavior. We find two key results: one theoretical and one empirical. First, unlike spot options, some futures options' early exercise probabilities and values do not correspond. Specifically, increased volatility raises the early exercise premium for in-the-money futures calls, but lowers the associated early exercise probability. Similarly, increasing the domestic interest rate raises the futures put early exercise premium, while lowering the associated early exercise probability. Second, observed early exercise experience of Philadelphia Stock Exchange spot options and Chicago Mercantile Exchange futures options is consistent with optimal early exercise behavior prescribed by a standard American option pricing model. Both types of option exercise events occur at or near the modeled early exercise boundaries.
Download or read book The Complete Guide to Option Pricing Formulas written by Espen Gaarder Haug and published by Professional Finance & Investment. This book was released on 2007-01-08 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accompanying CD-ROM contains ... "all pricing formulas, with VBA code and ready-to-use Excel spreadsheets and 3D charts for Greeks (or Option Sensitivities)."--Jacket.
Download or read book The Optimal Exercising Problem from American Options written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The fast advancement in computer technologies in the recent years has made the use of simulation to estimate stock/equity performances and pricing possible; however, determining the optimal exercise time and prices of American options using Monte-Carlo simulation is still a computationally challenging task due to the involved computer memory and computational complexity requirements. At each time step, the investor must decide whether to exercise the option to get the immediate payoff, or hold on to the option until a later time. Traditionally, the stock options are simulated using Monte-Carlo methods and all stock prices along the path are stored, and then the optimal exercise time is determined starting at the final time period and continuing backward in time. Also, as the number of paths simulated increases, the number of simultaneous equations that need to be solved at each time step grow proportionally. Currently, two theoretical methods have emerged in determining the optimal exercise problem. The first method uses the concept of least-squares approach in linear regression to estimate the value of continuing to hold on to the option via a set of randomly generated future stock prices. Then, the value of continuing can be compared to the payoff at current time from exercising the option and a decision can be reached, which gives the investor a higher value. The second method uses the finite difference approach to establish an exercise boundary for the American option via an artificially generated mesh on both possible stock prices and decision times. Then, the stock price is simulated and the method checks to see if it is inside the exercise boundary. In this research, these two solution approaches are evaluated and compared using discrete event simulation. This allows complex methods to be simulated with minimal coding efforts. Finally, the results from each method are compared. Although a more conservative method cannot be determined, the least-squares method is faster, more concise, easier to implement, and requires less memory than the mesh method. The motivation for this research stems from interest in simulating and evaluating complicated solution methods to the optimal exercise problem, yet requiring little programming effort to produce accurate and efficient estimation results.
