Download or read book Weighted Monte Carlo with Least Squares and Randomized Extended Kaczmarz for Option Pricing written by Damir Filipović and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 The Robustness of GARCH Option Pricing by the Least squares Monte Carlo Simulation written by 劉乃誠 and published by . This book was released on 2005 with total page 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 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 The Valuation of Real Options with the Least Squares Monte Carlo Simulation Method written by Artur Rodrigues and published by . This book was released on 2006 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a detailed analysis of the Least Squares Monte Carlo Simulation Method (Longstaff and Schwartz, 2001) and of the extension of Gamba (2003) to value portfolios of real options. The accuracy of the method is assessed when valuing stylised real options as maximum, compound or mutually exclusive options. For the latter, we propose an improved algorithm that is faster, more accurate as well as more reliable. The analysis is carried out for a large number of call and put options. It is done comparing alternative polynomial families and simulation methods, including moment matching techniques and low-discrepancy sequences. Unlike previous analysis of the method, our results suggest that the use of weighted Laguerre polynomials, initially proposed by Longstaff and Schwartz (2001), produces more accurate estimates. We show also that the choice of the best simulation method is contingent on the problem in hand. Low-discrepancy sequences tend to produce more accurate estimates, using fewer paths than pseudo-random numbers. The accuracy of the method depends on the payoff function and seems to converge, increasing both the number of basis and the number of simulated paths.

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 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 On Improving the Least Squares Monte Carlo Option Valuation Method written by Nelson Areal and published by . This book was released on 2018 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies various possible approaches to improving the least squares Monte Carlo option valuation method. We test different regression algorithms and suggest a variation to estimating the option continuation value, which can reduce the execution time of the algorithm by one third. We test the choice of varying polynomial families with different number of basis functions. We compare several variance reduction techniques, and find that using low discrepancy sequences can improve the accuracy up to four times. We also extend our analysis to compound and mutually exclusive options. For the latter, we propose an improved algorithm which is faster and more accurate.

Download or read book Convergence of the Least Squares Monte Carlo Approach to American Option Valuation written by and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 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 Assessing Least Squares Monte Carlo for the Kulatilaka Trigeorgis General Real Options Pricing Model written by Giuseppe Alesii and published by . This book was released on 2008 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: We assess the applicability of (Longstaff and Schwartz, 2001) Least Squares Monte Carlo method to the General Real Options Pricing Model of (Kulatilaka and Trigeorgis, 1994). We study LSMC under different stochastic processes: GBM, up to three dimensions, models 1, 2 and 3 in (Schwartz, 1997), benchmarking every application by lattice methods. We explore empirically a generalization of proposition 1 page 124 in (Longstaff and Schwartz, 2001) with respect to the number of discretization points, of basis functions and the number of simulated paths. We study the speed precision tradeoff of LSMC individual estimates. Finally, we show their statistical properties.

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 Weighted Monte Carlo and Pricing American Options written by Bin Yu and published by . This book was released on 2003 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Pricing American Options with Jump diffusion by Monte Carlo Simulation written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years the stock markets have shown tremendous volatility with significant spikes and drops in the stock prices. Within the past decade, there have been numerous jumps in the market; one key example was on September 17, 2001 when the Dow industrial average dropped 684 points following the 9-11 attacks on the United States. These evident jumps in the markets show the inaccuracy of the Black-Scholes model for pricing options. Merton provided the first research to appease this problem in 1976 when he extended the Black-Scholes model to include jumps in the market. In recent years, Kou has shown that the distribution of the jump sizes used in Merton's model does not efficiently model the actual movements of the markets. Consequently, Kou modified Merton's model changing the jump size distribution from a normal distribution to the double exponential distribution. Kou's research utilizes mathematical equations to estimate the value of an American put option where the underlying stocks follow a jump-diffusion process. The research contained within this thesis extends on Kou's research using Monte Carlo simulation (MCS) coupled with least-squares regression to price this type of American option. Utilizing MCS provides a continuous exercise and pricing region which is a distinct difference, and advantage, between MCS and other analytical techniques. The aim of this research is to investigate whether or not MCS is an efficient means to pricing American put options where the underlying stock undergoes a jump-diffusion process. This thesis also extends the simulation to utilize copulas in the pricing of baskets, which contains several of the aforementioned type of American options. The use of copulas creates a joint distribution from two independent distributions and provides an efficient means of modeling multiple options and the correlation between them. The research contained within this thesis shows that MCS provides a means of accurately pricing American put options where the underlying stock follows a jump-diffusion. It also shows that it can be extended to use copulas to price baskets of options with jump-diffusion. Numerical examples are presented for both portions to exemplify the excellent results obtained by using MCS for pricing options in both single dimension problems as well as multidimensional problems.

Download or read book Monte Carlo Methods written by Roman Frey and published by . This book was released on 2009-10 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides an extensive treatment of the entire Monte Carlo simulation theory. Furthermore, the Monte Carlo technique is used for addressing the pricing of various interest rate derivatives in different term structure models by the simulation approach. With the rising complexity and diversity of upcoming derivative securities, analytically tractable or closed-form pricing methods are difficult to find or even inexistent. If the thoroughly popular lattice valuation approach additionally fails due to non-recombining characteristics, Monte Carlo simulation represents a powerful and flexible alternative pricing method. The goal of this paper is to discuss and implement the fundamentals of Monte Carlo methods and to introduce the wide use of this approach in finance, especially in interest rate derivative valuation. The paper is roughly divided into three parts. The first part focuses on random number generation and on increasing efficiency methods for Monte Carlo, such as variance reduction techniques or low-discrepancy sequences. In the following part different term structure models are developed and the link to the simulation theory is eventually established. In the third and final part some ordinary and extended Monte Carlo algorithms are implemented and corresponding simulations are run in order to analyze Bermudan swaption prices in detail. Even though Monte Carlo methods feature a relatively slow but given convergence rate, they remain a competitive tool in financial applications. They owe their rising popularity to a large extent to their flexibility and to recent progress in methods which improve their accuracy and precision in estimating quantities of interest. Moreover, some of the leading yield curve models are heavily relying on Monte Carlo techniques. Several extensions of the standard Monte Carlo approach, such as least-squares Monte Carlo, for instance, are able to overcome the early-exercise hurdle a.