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Author : Lukas Müller
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (122 download)
Download or read book The Least-squares Monte Carlo Method for Pricing Bermudan Options in the Heston Model written by Lukas Müller and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : 黃惠君
Publisher :
ISBN 13 :
Total Pages : 102 pages
Book Rating : 4.:/5 (62 download)
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:
Author : Alfredo Ibañez
Publisher :
ISBN 13 :
Total Pages : 50 pages
Book Rating : 4.:/5 (13 download)
Download or read book The Optimal Method for Pricing Bermudan Options by Simulation written by Alfredo Ibañez and published by . This book was released on 2017 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: Least-squares methods enable us to price Bermudan-style options by Monte Carlo simulation. They are based on estimating the option continuation value by least squares. We show that the Bermudan price is maximized when this continuation value is estimated near the exercise boundary, which is equivalent to implicitly estimating the optimal exercise boundary by using the value-matching condition. Localization is the key difference with respect to global regression methods, but is fundamental for optimal exercise decisions, and requires estimation of the continuation value by iterating local least-squares (because we estimate and localize the exercise boundary at the same time). In the numerical example, in agreement with this optimality, the new prices or lower bounds (i) improve upon the prices reported by other methods and (ii) are very close to the associated dual upper bounds. We also study the method's convergence.
Author :
Publisher :
ISBN 13 :
Total Pages : 152 pages
Book Rating : 4.E/5 ( download)
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:
Author : Ralf Korn
Publisher : CRC Press
ISBN 13 : 1420076191
Total Pages : 485 pages
Book Rating : 4.4/5 (2 download)
Download or read book Monte Carlo Methods and Models in Finance and Insurance written by Ralf Korn and published by CRC Press. This book was released on 2010-02-26 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering a unique balance between applications and calculations, Monte Carlo Methods and Models in Finance and Insurance incorporates the application background of finance and insurance with the theory and applications of Monte Carlo methods. It presents recent methods and algorithms, including the multilevel Monte Carlo method, the statistical Rom
Author : Diego Garcia
Publisher :
ISBN 13 :
Total Pages : 132 pages
Book Rating : 4.:/5 (34 download)
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:
Author : Phuc Phan
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (13 download)
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.
Author : Alberto Barola
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659352607
Total Pages : 160 pages
Book Rating : 4.3/5 (526 download)
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.
Author : David Farahany
Publisher :
ISBN 13 :
Total Pages : 38 pages
Book Rating : 4.:/5 (13 download)
Download or read book Mixing LSMC and PDE Methods to Price Bermudan Options written by David Farahany and published by . This book was released on 2020 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets under stochastic volatility. The algorithm is formulated for an arbitrary number of assets and volatility processes and we prove the algorithm converges almost surely for a class of models. We also introduce a multi-level Monte-Carlo/multi-grid method to improve the algorithm's computational complexity. Our numerical examples focus on the single (2d) and multi-dimensional (4d) Heston models and we compare our hybrid algorithm with classical LSMC approaches. In each case, we find that the hybrid algorithm outperforms standard LSMC in terms of estimating prices and optimal exercise boundaries.
Author : 劉乃誠
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)
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:
Author : Bhojnarine Rambharat
Publisher :
ISBN 13 :
Total Pages : 43 pages
Book Rating : 4.:/5 (13 download)
Download or read book Sequential Monte Carlo Pricing of American-Style Options Under Stochastic Volatility Models written by Bhojnarine Rambharat and published by . This book was released on 2013 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the optimal decision functions in the corresponding dynamic programming problem can be expressed as functions of conditional distributions of volatility, given observed data. By constructing statistics summarizing information about these conditional distributions, one can obtain high quality approximate solutions. Although the required conditional distributions are in general intractable, they can be arbitrarily precisely approximated using sequential Monte Carlo schemes. The drawback, as with many Monte Carlo schemes, is potentially heavy computational demand. We present two variants of the algorithm, one closely related to the well-known least-squares Monte Carlo algorithm of Longstaff and Schwartz (2001), and the other solving the same problem using a “brute force” gridding approach. We estimate an illustrative SV model using Markov chain Monte Carlo (MCMC) methods for three equities. We also demonstrate the use of our algorithm by estimating posterior distributions of the market price of volatility risk for each of the three equities.
Author : Gilles B. Desvilles
Publisher :
ISBN 13 :
Total Pages : 14 pages
Book Rating : 4.:/5 (129 download)
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.
Author : Roman Frey
Publisher :
ISBN 13 : 9783639204018
Total Pages : 136 pages
Book Rating : 4.2/5 (4 download)
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.
Download or read book Pricing Swing Options within Stochastic Volatility Model by Least Square Monte Carlo written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Giuseppe Alesii
Publisher :
ISBN 13 :
Total Pages : 88 pages
Book Rating : 4.:/5 (129 download)
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.
Author : Nelson Areal
Publisher :
ISBN 13 :
Total Pages : 36 pages
Book Rating : 4.:/5 (129 download)
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.
Author : Damir Filipović
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (117 download)
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:
