Download or read book Pricing American Options by Canonical Least Squares Monte Carlo written by Qiang Liu and published by . This book was released on 2008 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: Options pricing and hedging under canonical valuation have recently been demonstrated to be quite effective, but unfortunately are only applicable to European options. In this paper, a variation of canonical valuation called canonical least-squares Monte Carlo is proposed to price American options, which proceeds in three stages. First, given a set of historical gross returns (or price ratios) of the underlying for a chosen time interval, a discrete risk-neutral distribution is obtained via the canonical approach. Second, from this canonical distribution independent random samples of gross returns are taken to simulate future price paths for the underlying. Third, to those paths the least-squares Monte Carlo method is then applied to compute a price for an American option. Numerical results obtained from using simulated gross returns under geometric Brownian motion (GBM) show that this new approach yields reasonably accurate prices for American put options and can be utilized as an alternative to pricing American options, whether the underlying follows GBM or not.

Download or read book Numerical study to least squares monte carlo method for pricing american options written by 黃惠君 and published by . This book was released on 2003 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Approving Least Squares Monte Carlo Approach for Valuing American Options written by Lei Zhang and published by . This book was released on 2004 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book On the Robustness of Least Squares Monte Carlo LSM for Pricing American Derivatives written by Manuel Moreno and published by . This book was released on 2007 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper analyses the robustness of Least - Squares Monte Carlo, a technique proposed by Longstaff and Schwartz (2001) for pricing American options. This method is based on least - squares regressions in which the explanatory variables are certain polynomial functions. We analyze the impact of different basis functions on option prices. Numerical results for American put options show that this approach is quite robust to the choice of basis functions. For more complex derivatives, this choice can slightly affect option prices.

Download or read book Assessing the Least Squares Monte Carlo Approach to American Option Valuation written by Lars Stentoft and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book American Type Options written by Dmitrii S. Silvestrov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-12-17 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematical presentation of stochastic approximation methods for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The volume presents results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.

Download or read book Convergence of the Least Squares Monte Carlo Approach to American Option Valuation written by Lars Stentoft and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Least Squares Monte Carlo and Quasi Monte Carlo Method in Pricing American Put Options Using Matlab written by Phuc Phan and published by . This book was released on 2016 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this report, we evaluate the use of the Least Squares Monte Carlo (LSM) method, which was proposed by Longstaff and Schwartz in 2001. The holder of an American option has the right to exercise the option anytime, which makes the option much more difficult to price compared to a European style option. LSM is a simple and powerful method to price American style options and utilizes the use of least squares to estimate the conditional expected payoff to the option holder from continuation value. I provide a simple version of the LSM algorithm using second degree polynomials as basis functions with working code in Matlab to price American put option. I illustrate how the model is affected when input parameter such as risk free interest rate, volatility, underlying stock price, time to maturity are perturbed. After that, I construct the quasi Monte Carlo version of the Least Square algorithm by using Halton sequence and compare the performance of both quasi Monte Carlo and Monte Carlo algorithm.

Download or read book Valuing American Options by Simulation written by Laura Hass Thomsen and published by . This book was released on 2015 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Valuing Bermuda Asian Options by Least Squares Monte Carlo Simulation written by and published by . This book was released on 2007 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Cost of Accuracy in the Least Squares Monte Carlo Approach written by Gilles B. Desvilles and published by . This book was released on 2011 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article follows in the footsteps of Longstaff and Schwartz' seminal article about the use of regressions to model expectations in the valuation of American options with Monte Carlo simulation. The article repeats the original American put pricing in order to check for estimation accuracy and computation speed.In addition the article investigates the use of the control variate technique in order to accelerate the Least Squares Monte Carlo simulation, and implements a way to get the delta sensitivity without much raising the response time. However the results underline what is believed to be the main impediment of the approach: the cost of accuracy. Performed in dimension one on a standard computer the simulations lead to conclude that pricing an option agrave; la Longstaff Schwartz is not advised when the option is simple enough to be valued with a recombining binomial tree. Indeed the response times of the binomial pricing are incomparably shorter. Moreover the standard error proposed by the method under study is not reliable both in theory and in practice. There remains a mere conjecture according to which when increasing significantly the number of trajectories then convergence to the true price is reached and the estimated standard error is negligible. But, due to the involved pathwise regressions, such an increase would lengthen considerably the response time.Finally hope comes from computer improvements, especially in the memory field. In the least resource-consuming cases running the simulation with much more trajectories on a recent computer ends up yielding the true prices with no surrounding uncertainty and in a reasonable time. Hence, for similar pricings, one can expect to rely on the estimated standard error to tell when the simulation has converged.

Download or read book Valuing American Asian Options with Least Squares Monte Carlo and Low Discrepancy Sequences written by Andries Jacobus Van Niekerk and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: There exists no closed form approximation for arithmetically calculated Asian options, but research has shown that closed form approximations are possible for Geometrically calculated Asian options. The aim of this dissertation is to effectively price American Asian options with the least squares Monte Carlo approach (Longstaff & Schwartz, 2001), applying Low discrepancy sequences and variance reduction techniques. We evaluate how these techniques affect the pricing of American options and American Asian options in terms of accuracy, computational efficiency, and computational time used to implement these techniques. We consider the effect of, Laguerre-, weighted Laguerre- , Hermite-, and Monomial-basis functions on the Longstaff and Schwartz (2001) model. We briefly investigate GPU optimization of the Longstaff and Schwartz algorithm within Matlab. We also graph the associated implied and Local volatility surfaces of the American Asian options to assist in the practical applicability of these options.

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:

Download or read book Optimum Weighting for the Least Squares Monte Carlo Approach to American Options Under the CEV Model written by Jason Barden and published by . This book was released on 2015 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we propose the optimum weighting scheme for pricing American options under a local volatility model. American options are priced under the constant elasticity of variance volatility model using Monte Carlo simulation. The residuals obtained from regression were heteroscedastic. For spot prices deep out-of-the-money, alternate weighting methods were found to provide improved accuracy over ordinary least squares. For spot prices deep in-the-money, the residuals were also heteroscedastic, however, the number of residuals present in the regression dominated and ordinary least squares provided improved accuracy. Generalised least squares was found to proved the most accurate overall weighting method.

Download or read book American Option Pricing Under Stochastic Volatility written by Suchandan Guha and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: ABSTRACT: We developed two new numerical techniques to price American options when the underlying follows a bivariate process. The first technique exploits the semi-martingale representation of an American option price together with a coarse approximation of its early exercise surface that is based on an efficient implementation of the least-squares Monte Carlo method. The second technique exploits recent results in the efficient pricing of American options under constant volatility. Extensive numerical evaluations show these methods yield very accurate prices in a computationally efficient manner with the latter significantly faster than the former. However, the flexibility of the first method allows for its extension to a much larger class of optimal stopping problems than addressed in this paper.

Download or read book Least Squares Monte Carlo GARCH Methods for American Options written by Lars Stentoft and published by . This book was released on 2004 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: