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Addressing The Bias In Monte Carlo Pricing Of Multi Asset Options With Multiple Barriers Through Discrete Sampling
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Book Synopsis Addressing the Bias in Monte Carlo Pricing of Multi-Asset Options with Multiple Barriers Through Discrete Sampling by : Pavel V. Shevchenko
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.
Book Synopsis Financial Engineering with Finite Elements by : Juergen Topper
Download or read book Financial Engineering with Finite Elements written by Juergen Topper and published by John Wiley & Sons. This book was released on 2005-06-24 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: The pricing of derivative instruments has always been a highly complex and time-consuming activity. Advances in technology, however, have enabled much quicker and more accurate pricing through mathematical rather than analytical models. In this book, the author bridges the divide between finance and mathematics by applying this proven mathematical technique to the financial markets. Utilising practical examples, the author systematically describes the processes involved in a manner accessible to those without a deep understanding of mathematics. * Explains little understood techniques that will assist in the accurate more speedy pricing of options * Centres on the practical application of these useful techniques * Offers a detailed and comprehensive account of the methods involved and is the first to explore the application of these particular techniques to the financial markets
Book Synopsis Monte Carlo and Quasi-Monte Carlo Methods 2010 by : Leszek Plaskota
Download or read book Monte Carlo and Quasi-Monte Carlo Methods 2010 written by Leszek Plaskota and published by Springer Science & Business Media. This book was released on 2012-08-23 with total page 721 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the refereed proceedings of the Ninth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Warsaw (Poland) in August 2010. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance and statistics.
Book Synopsis Recent Developments in Computational Finance by : Thomas Gerstner
Download or read book Recent Developments in Computational Finance written by Thomas Gerstner and published by World Scientific. This book was released on 2013 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational finance is an interdisciplinary field which joins financial mathematics, stochastics, numerics and scientific computing. Its task is to estimate as accurately and efficiently as possible the risks that financial instruments generate. This volume consists of a series of cutting-edge surveys of recent developments in the field written by leading international experts. These make the subject accessible to a wide readership in academia and financial businesses. The book consists of 13 chapters divided into 3 parts: foundations, algorithms and applications. Besides surveys of existing results, the book contains many new previously unpublished results.
Book Synopsis The Journal of Computational Finance by :
Download or read book The Journal of Computational Finance written by and published by . This book was released on 2002 with total page 1014 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Financial Engineering with Finite Elements by : Jürgen Topper
Download or read book Financial Engineering with Finite Elements written by Jürgen Topper and published by John Wiley & Sons. This book was released on 2005-04 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: The pricing of derivative instruments has always been a highly complex and time-consuming activity. Advances in technology, however, have enabled much quicker and more accurate pricing through mathematical rather than analytical models. In this book, the author bridges the divide between finance and mathematics by applying this proven mathematical technique to the financial markets. Utilising practical examples, the author systematically describes the processes involved in a manner accessible to those without a deep understanding of mathematics. * Explains little understood techniques that will assist in the accurate more speedy pricing of options * Centres on the practical application of these useful techniques * Offers a detailed and comprehensive account of the methods involved and is the first to explore the application of these particular techniques to the financial markets
Book Synopsis Monte Carlo Methods and Path-Generation Techniques for Pricing Multi-Asset Path-Dependent Options by : Piergiacomo Sabino
Download or read book Monte Carlo Methods and Path-Generation Techniques for Pricing Multi-Asset Path-Dependent Options written by Piergiacomo Sabino and published by . This book was released on 2007 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the problem of pricing path-dependent options on a basket of underlying assets using simulations. As an example we develop our studies using Asian options.Asian options are derivative contracts in which the underlying variable is the average price of given assets sampled over a period of time. Due to this structure, Asian options display a lower volatility and are therefore cheaper than their standard European counterparts.This paper is a survey of some recent enhancements to improve efficiency when pricing Asian options by Monte Carlo simulation in the Black-Scholes model. We analyze the dynamics with constant and time-dependent volatilities of the underlying asset returns.We present a comparison between the precision of the standard Monte Carlo method (MC) and the stratified Latin Hypercube Sampling (LHS). In particular, we discuss the use of low-discrepancy sequences, also known as Quasi-Monte Carlo method (QMC), and a randomized version of these sequences, known as Randomized Quasi Monte Carlo (RQMC). The latter has proven to be a useful variance reduction technique for both problems of up to 20 dimensions and for very high dimensions.Moreover, we present and test a new path generation approach based on a Kronecker product approximation (KPA) in the case of time-dependent volatilities. KPA proves to be a fast generation technique and reduces the computational cost of the simulation procedure.
Book Synopsis Valuation of Barrier Options Using Sequential Monte Carlo by : Pavel V. Shevchenko
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.
Book Synopsis Using Monte Carlo Simulation and Importance Sampling to Rapidly Obtain Jump-Diffusion Prices of Continuous Barrier Options by : Mark S. Joshi
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.
Book Synopsis Using Monte Carlo Simulation and Importance Sampling to Rapidly Obtain Jump-diffusion Prices of Continuous Barrier Options by : Mark Suresh Joshi
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:
Book Synopsis Sequential Monte Carlo Methods in Practice by : Arnaud Doucet
Download or read book Sequential Monte Carlo Methods in Practice written by Arnaud Doucet and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods are revolutionizing the on-line analysis of data in many fileds. They have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques.
Book Synopsis Multi-level Monte Carlo Simulations with Importance Sampling by : Przemyslaw Stan Stilger
Download or read book Multi-level Monte Carlo Simulations with Importance Sampling written by Przemyslaw Stan Stilger and published by . This book was released on 2013 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Monte Carlo Approaches to Multi-asset Options by : 謝佳良
Download or read book Monte Carlo Approaches to Multi-asset Options written by 謝佳良 and published by . This book was released on 1999 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Barrier Option Pricing Under SABR Model Using Monte Carlo Methods by : Junling Hu
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.
Book Synopsis A Monte Carlo Method for Pricing American Options by : Diego Garcia
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:
Book Synopsis Efficient Monte Carlo and Quasi-Monte Carlo Pricing of Multi-barrier Reverse Convertibles by : Carlos Ungil
Download or read book Efficient Monte Carlo and Quasi-Monte Carlo Pricing of Multi-barrier Reverse Convertibles written by Carlos Ungil and published by . This book was released on 2008 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A General Closed Form Approximation Pricing Formula for Basket and Multi-Asset Spread Options by : Tommaso Pellegrino
Download or read book A General Closed Form Approximation Pricing Formula for Basket and Multi-Asset Spread Options written by Tommaso Pellegrino and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The aims of this paper are twofold. Firstly, we present an approximating formula for pricing basket and multi-asset spread options, which genuinely extends Caldana and Fusai (2013) two-asset spread options formula. Secondly, under the lognormal setting, we show that our formula becomes a Black and Scholes type formula, extending Bjerksund and Stensland (2011). Numerical experiments and comparison with Monte Carlo simulations and other methods available in the literature are discussed. The main contribution of this paper is to provide practitioners with a pricing formula, which can be used for pricing basket and multi-asset spread options, even under a non-Gaussian framework.
