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Author : Simon Hatzesberger
Publisher :
ISBN 13 :
Total Pages : 76 pages
Book Rating : 4.:/5 (785 download)
Download or read book Unbiased Monte Carlo estimation for barrier option pricing written by Simon Hatzesberger and published by . This book was released on 2011 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Pavel V. Shevchenko
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (13 download)
Download or read book Valuation of Barrier Options Using Sequential Monte Carlo written by Pavel V. Shevchenko and published by . This book was released on 2015 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sequential Monte Carlo (SMC) methods have successfully been used in many applications in engineering, statistics and physics. However, these are seldom used in financial option pricing literature and practice. This paper presents SMC method for pricing barrier options with continuous and discrete monitoring of the barrier condition. Under the SMC method, simulated asset values rejected due to barrier condition are re-sampled from asset samples that do not breach the barrier condition improving the efficiency of the option price estimator; while under the standard Monte Carlo many simulated asset paths can be rejected by the barrier condition making it harder to estimate option price accurately. We compare SMC with the standard Monte Carlo method and demonstrate that the extra effort to implement SMC when compared with the standard Monte Carlo is very little while improvement in price estimate can be significant. Both methods result in unbiased estimators for the price converging to the true value as 1/ sqrt{M}$, where $M$ is the number of simulations (asset paths). However, the variance of SMCestimator is smaller and does not grow with the number of time steps when compared to the standard Monte Carlo. In this paper we demonstrate that SMC can successfully be used for pricing barrier options. SMC can also be used for pricing other exotic options and also for cases with many underlying assets and additional stochastic factors such as stochastic volatility; we provide general formulas and references.
Author : Mark S. Joshi
Publisher :
ISBN 13 :
Total Pages : 15 pages
Book Rating : 4.:/5 (129 download)
Download or read book Using Monte Carlo Simulation and Importance Sampling to Rapidly Obtain Jump-Diffusion Prices of Continuous Barrier Options written by Mark S. Joshi and published by . This book was released on 2007 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of pricing a continuous barrier option in a jump-diffusion model is studied. It is shown that via an effective combination of importance sampling and analytic formulas thatsubstantial speed ups can be achieved. These techniques are shown to be particularly effective for computing deltas.
Author : Sheldon Ross
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Efficient Monte Carlo Barrier Option Pricing When the Underlying Security Price Follows a Jump-Diffusion Process written by Sheldon Ross and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We present efficient simulation procedures for pricing barrier options when the underlying security price follows a geometric Brownian motion with jumps. Metwally and Atiya [2002] developed a simulation approach for pricing knock-out options in the same setting, but no variance reduction was introduced. We improve upon Metwally and Atiya's method by innovative applications of well-known variance reduction techniques. We also show how to use simulation to price knock-in options. Numerical examples show that our proposed Monte Carlo procedures lead to substantial variance reduction as well as a reduction in computing time.
Author : Pokpong Chirayukool
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (921 download)
Download or read book The Valuation of Exotic Barrier Options and American Options Using Monte Carlo Simulation written by Pokpong Chirayukool and published by . This book was released on 2011 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mark Suresh Joshi
Publisher :
ISBN 13 : 9780734035721
Total Pages : 14 pages
Book Rating : 4.0/5 (357 download)
Download or read book Using Monte Carlo Simulation and Importance Sampling to Rapidly Obtain Jump-diffusion Prices of Continuous Barrier Options written by Mark Suresh Joshi and published by . This book was released on 2006 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Don L. McLeish
Publisher : John Wiley & Sons
ISBN 13 : 1118160940
Total Pages : 308 pages
Book Rating : 4.1/5 (181 download)
Download or read book Monte Carlo Simulation and Finance written by Don L. McLeish and published by John Wiley & Sons. This book was released on 2011-09-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods have been used for decades in physics, engineering, statistics, and other fields. Monte Carlo Simulation and Finance explains the nuts and bolts of this essential technique used to value derivatives and other securities. Author and educator Don McLeish examines this fundamental process, and discusses important issues, including specialized problems in finance that Monte Carlo and Quasi-Monte Carlo methods can help solve and the different ways Monte Carlo methods can be improved upon. This state-of-the-art book on Monte Carlo simulation methods is ideal for finance professionals and students. Order your copy today.
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 : Junling Hu
Publisher :
ISBN 13 :
Total Pages : 170 pages
Book Rating : 4.:/5 (891 download)
Download or read book Barrier Option Pricing Under SABR Model Using Monte Carlo Methods written by Junling Hu and published by . This book was released on 2013 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The project investigates the prices of barrier options from the constant underlying volatility in the Black-Scholes model to stochastic volatility model in SABR framework. The constant volatility assumption in derivative pricing is not able to capture the dynamics of volatility. In order to resolve the shortcomings of the Black-Scholes model, it becomes necessary to find a model that reproduces the smile effect of the volatility. To model the volatility more accurately, we look into the recently developed SABR model which is widely used by practitioners in the financial industry. Pricing a barrier option whose payoff to be path dependent intrigued us to find a proper numerical method to approximate its price. We discuss the basic sampling methods of Monte Carlo and several popular variance reduction techniques. Then, we apply Monte Carlo methods to simulate the price of the down-and-out put barrier options under the Black-Scholes model and the SABR model as well as compare the features of these two models.
Download or read book Variance Reduction for Monte Carlo Simulation of European, American Or Barrier Options in a Stochastic Volatility Environment written by and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work we develop a methodology to reduce the variance when applying Monte Carlo simulation to the pricing of a European, American or Barrier option in a stochastic volatility environment. We begin by presenting some applicable concepts in the theory of stochastic differential equations. Secondly, we develop the model for the evolution of an asset price under constant volatility. We next present the replicating portfolio and equivalent martingale measure approaches to the pricing of a European style option. Modeling an asset price utilizing constant volatility has been shown to be an inefficient model[8,16]. One way to compensate for this inefficiency is the use of stochastic volatility models, which involves modeling the volatility as a function of a stochastic process[26]. A class of these models is presented and a discussion is given on how to price European options in this framework. After developing the methods of how to price, we begin our discussion on Monte Carlo simulation of European options in a stochastic volatility environment. We start by describing how to simulate Monte Carlo for a diffusion process modeled as a stochastic differential equation. The essential element to our variance reduction technique, which is known as importance sampling, is hereafter presented. Importance sampling requires a preliminary approximation to the expectation of interest, which we obtain by a fast mean-reversion expansion of the pricing partial differential equation[22,6]. A detailed discussion is given on this fast mean-reversion expansion technique, which was first presented in [10]. We shall compare utilizing this method of expansion with that developed in [11], which is know as small noise expansion, and demonstrate numerically the efficiency of the fast mean-reversion expansion, in particular in the presence of a skew. We next wish to apply our variance reduction technique to the pricing of an American and barrier option. A discussion is given on how to price.
Author : Charles J. Mode
Publisher : IntechOpen
ISBN 13 : 9789533074276
Total Pages : 440 pages
Book Rating : 4.0/5 (742 download)
Download or read book Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science written by Charles J. Mode and published by IntechOpen. This book was released on 2011-02-28 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an eclectic mix of applications of Monte Carlo methods in many fields of research should not be surprising, because of the ubiquitous use of these methods in many fields of human endeavor. In an attempt to focus attention on a manageable set of applications, the main thrust of this book is to emphasize applications of Monte Carlo simulation methods in biology and medicine.
Author : Emmanuel Deogratias
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659362316
Total Pages : 124 pages
Book Rating : 4.3/5 (623 download)
Download or read book Methods for Pricing and Hedging Plain Vanilla Barrier Options written by Emmanuel Deogratias and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Black Scholes Model (1973) is used to price and hedge plain vanilla barrier options on a non dividend paying asset. Under this model, Monte Carlo Simulation, Stratified sampling, Simpson's rule, Trapezoidal rule and Antithetic variable techniques have been used to determine the value and hedging portfolio of a plain vanilla barrier option. Also stochastic dynamic programming has been developed so as to determine the price and hedging portfolio of the option. Finally the methods are compared to each other in terms of accuracy. It is found that stratified sampling technique is the best method after comparing with other methods.
Author : Tracey Andrew Tullie
Publisher :
ISBN 13 :
Total Pages : 115 pages
Book Rating : 4.:/5 (52 download)
Download or read book Variance Reduction for Monte Carlo Simulation of European, American Or Barrier Options in a Stochastic Volatility Environment written by Tracey Andrew Tullie and published by . This book was released on 2002 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: Keywords: importance sampling, variance reduction, volatility, fast mean-reverting asymptotics.
Download or read book Efficient Monte Carlo and Quasi-Monte Carlo Option Pricing Under the Variance-Gamma Model written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop and study efficient Monte Carlo algorithms for pricing path-dependent options with the variance gamma model. The key ingredient is difference-of-gamma bridge sampling, based on the representation of a variance gamma process as the difference of two increasing gamma processes. For typical payoff structures, we obtain a pair of estimators (named low and high) with expectations that are (i) monotone along any such bridge sampler; (ii) contain the continuous-time price. These estimators provide pathwise bounds on unbiased estimators that would be more expensive to compute (infinitely expensive in some situations). By using these bounds together with extrapolation techniques, we obtain significant simulation efficiency improvements by work reduction. We then combine the gamma bridge sampling with randomized quasi-Monte Carlo to reduce the variance and thus improve the efficiency by another important factor. We illustrate the large efficiency improvements on numerical examples for Asian, lookback, and barrier options.
Author : Padriac Walsh
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (264 download)
Download or read book Option Pricing Using Monte Carlo Simulation written by Padriac Walsh and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andreas Gabler
Publisher :
ISBN 13 :
Total Pages : 25 pages
Book Rating : 4.:/5 (13 download)
Download or read book Pricing, Loss and Sensitivity Analysis of Barrier Options Via Regression written by Andreas Gabler and published by . This book was released on 2018 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo simulation methods for the valuation of financial instruments have become a staple of empirical economic analysis. A specific focus is dedicated to the feasibility of the stock price losses and barrier options as well as the sensitivity of partial time barrier options in dependence on their barrier values, which, to the best of our knowledge, hasn't been analysed in academic papers so far. This paper compares the performance of analytical results with empirical regression-based Monte Carlo outcomes, as proposed by Broadie et. al. (2015), where outer stage samples are used to generate financial risk factors and an inner stage simulation is applied to price the barrier options given the outer stage scenarios. Furthermore, potential correlation characteristics between portfolio pricing and loss regarding infinitesimal small changes in the underlying asset (Delta) are exhibited. Thus, a theoretical assumption approach to the explicit loss function is considered, as yet such an analytical loss function has not occurred in related literature.
Author : Pavel V. Shevchenko
Publisher :
ISBN 13 :
Total Pages : 20 pages
Book Rating : 4.:/5 (13 download)
Download or read book Addressing the Bias in Monte Carlo Pricing of Multi-Asset Options with Multiple Barriers Through Discrete Sampling written by Pavel V. Shevchenko and published by . This book was released on 2014 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on the continuous-time extrema of an underlying asset. It is based on the simple and easy to implement analytic formulas for the distribution of one-dimensional Brownian Bridge extremes. This paper extends the technique to the valuation of multi-asset options with knock-out barriers imposed for all or some of the underlying assets. We derive formula for the unbiased option price estimator based on the joint distribution of the multi-dimensional Brownian Bridge dependent extrema. As analytic formulas are not available for the joint distribution in general, we develop upper and lower biased option price estimators based on the distribution of independent extrema and the Fréchet lower and upper bounds for the unknown distribution. All estimators are simple and easy to implement. They can always be used to bind the true value by a confidence interval. Numerical tests indicate that our biased estimators converge rapidly to the true option value as the number of time steps for the asset path simulation increases in comparison to the estimator based on the standard discrete-time method. The convergence rate depends on the correlation and barrier structures of the underlying assets.
