A Fast And Accurate Fft Based Method For Pricing Early Exercise Options Under Levy Processes

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A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options Under Levy Processes

Author : Roger Lord
Publisher :
ISBN 13 :
Total Pages : 23 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options Under Levy Processes by : Roger Lord

Download or read book A Fast and Accurate FFT-Based Method for Pricing Early-Exercise Options Under Levy Processes written by Roger Lord and published by . This book was released on 2007 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fast and accurate method for pricing early exercise and certain exotic options in computational finance is presented. The method is based on a quadrature technique and relies heavily on Fourier transformations. The main idea is to reformulate the well-known risk-neutral valuation formula by recognising that it is a convolution. The resulting convolution is dealt with numerically by using the Fast Fourier Transform (FFT). This novel pricing method, which we dub the Convolution method, CONV for short, is applicable to a wide variety of payoffs and only requires the knowledge of the characteristic function of the model. As such the method is applicable within exponential Leacute;vy models, including the exponentially affine jump-diffusion models. For an M-times exercisable Bermudan option, the overall complexity is O(MN log(N)) with N grid points used to discretise the price of the underlying asset. It is shown how to price American options efficiently by applying Richardson extrapolation to the prices of Bermudan options.

Efficient pricing algorithms for exotic derivatives

Author : Roger Lord
Publisher : Rozenberg Publishers
ISBN 13 : 9051709099
Total Pages : 211 pages
Book Rating : 4.0/5 (517 download)

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Book Synopsis Efficient pricing algorithms for exotic derivatives by : Roger Lord

Download or read book Efficient pricing algorithms for exotic derivatives written by Roger Lord and published by Rozenberg Publishers. This book was released on 2008 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Pricing Derivatives Under Lévy Models

Author : Andrey Itkin
Publisher : Birkhäuser
ISBN 13 : 1493967924
Total Pages : 318 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Pricing Derivatives Under Lévy Models by : Andrey Itkin

Download or read book Pricing Derivatives Under Lévy Models written by Andrey Itkin and published by Birkhäuser. This book was released on 2017-02-27 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a novel numerical approach to solving partial integro-differential equations arising in asset pricing models with jumps, which greatly exceeds the efficiency of existing approaches. The method, based on pseudo-differential operators and several original contributions to the theory of finite-difference schemes, is new as applied to the Lévy processes in finance, and is herein presented for the first time in a single volume. The results within, developed in a series of research papers, are collected and arranged together with the necessary background material from Lévy processes, the modern theory of finite-difference schemes, the theory of M-matrices and EM-matrices, etc., thus forming a self-contained work that gives the reader a smooth introduction to the subject. For readers with no knowledge of finance, a short explanation of the main financial terms and notions used in the book is given in the glossary. The latter part of the book demonstrates the efficacy of the method by solving some typical problems encountered in computational finance, including structural default models with jumps, and local stochastic volatility models with stochastic interest rates and jumps. The author also adds extra complexity to the traditional statements of these problems by taking into account jumps in each stochastic component while all jumps are fully correlated, and shows how this setting can be efficiently addressed within the framework of the new method. Written for non-mathematicians, this book will appeal to financial engineers and analysts, econophysicists, and researchers in applied numerical analysis. It can also be used as an advance course on modern finite-difference methods or computational finance.

Fourier Transform

Author : Salih Salih
Publisher : BoD – Books on Demand
ISBN 13 : 9535105183
Total Pages : 316 pages
Book Rating : 4.5/5 (351 download)

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Book Synopsis Fourier Transform by : Salih Salih

Download or read book Fourier Transform written by Salih Salih and published by BoD – Books on Demand. This book was released on 2012-04-25 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on Fourier transform applications in electromagnetic field and microwave, medical applications, error control coding, methods for option pricing, and Helbert transform application. It is hoped that this book will provide the background, reference and incentive to encourage further research and results in these fields as well as provide tools for practical applications. It provides an applications-oriented analysis written primarily for electrical engineers, control engineers, signal processing engineers, medical researchers, and the academic researchers. In addition the graduate students will also find it useful as a reference for their research activities.

Modeling the Short Rate as a Levy Process and Option Pricing with the FFT.

Author : Roy Zywina
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis Modeling the Short Rate as a Levy Process and Option Pricing with the FFT. by : Roy Zywina

Download or read book Modeling the Short Rate as a Levy Process and Option Pricing with the FFT. written by Roy Zywina and published by . This book was released on 2017 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper describes a practical algorithm for modeling interest rate derivatives with the short rate following a Levy process using the fast Fourier transform algorithm (FFT). It can be used with any Levy process for which we have a closed form formula for the characteristic function, this includes a large variety of 'fat-tailed' jump diffusion processes. This model allows for the computation of forward rates and can be used to price American and Bermudan exercise options. Pricing algorithms are provided for option bonds and swaptions. The model is effectively equivalent to a tree approach except that diffusion is done by FFT instead of by branching. Pricing algorithms using trees or finite difference method can be easily adapted. Under the Normal distribution it can replicate the single factor Hull-White and Black-Karasinski models. The model supports mean reversion of interest rates. Monte Carlo simulations can be efficiently performed as well.

Computational Science - ICCS 2007

Author : Yong Shi
Publisher : Springer
ISBN 13 : 3540725865
Total Pages : 1285 pages
Book Rating : 4.5/5 (47 download)

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Book Synopsis Computational Science - ICCS 2007 by : Yong Shi

Download or read book Computational Science - ICCS 2007 written by Yong Shi and published by Springer. This book was released on 2007-07-14 with total page 1285 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of a four-volume set, this book constitutes the refereed proceedings of the 7th International Conference on Computational Science, ICCS 2007, held in Beijing, China in May 2007. The papers cover a large volume of topics in computational science and related areas, from multiscale physics to wireless networks, and from graph theory to tools for program development.

Financial Econometrics Modeling: Derivatives Pricing, Hedge Funds and Term Structure Models

Author : G. Gregoriou
Publisher : Springer
ISBN 13 : 0230295207
Total Pages : 229 pages
Book Rating : 4.2/5 (32 download)

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Book Synopsis Financial Econometrics Modeling: Derivatives Pricing, Hedge Funds and Term Structure Models by : G. Gregoriou

Download or read book Financial Econometrics Modeling: Derivatives Pricing, Hedge Funds and Term Structure Models written by G. Gregoriou and published by Springer. This book was released on 2015-12-26 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proposes new tools and models to price options, assess market volatility, and investigate the market efficiency hypothesis. In particular, it considers new models for hedge funds and derivatives of derivatives, and adds to the literature of testing for the efficiency of markets both theoretically and empirically.

Prices and Sensitivities of Barrier and First-Touch Digital Options in Levy-Driven Models

Author : Mitya Boyarchenko
Publisher :
ISBN 13 :
Total Pages : 43 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Prices and Sensitivities of Barrier and First-Touch Digital Options in Levy-Driven Models by : Mitya Boyarchenko

Download or read book Prices and Sensitivities of Barrier and First-Touch Digital Options in Levy-Driven Models written by Mitya Boyarchenko and published by . This book was released on 2008 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a fast and accurate FFT-based method of computing the prices and sensitivities of barrier options and first-touch digital options on stocks whose log-price follows a Levy process. The numerical results obtained via our approach are demonstrated to be in good agreement with the results obtained using other (sometimes fundamentally different) approaches that exist in the literature. However, our method is computationally much faster (often, dozens of times faster). Moreover, our technique has the advantage that its application does not entail a detailed analysis of the underlying Levy process: one only needs an explicit analytic formula for the characteristic exponent of the process. Thus our algorithm is very easy to implement in practice. Finally, our method yields accurate results for a wide range of values of the spot price, including those that are very close to the barrier, regardless of whether the maturity period of the option is long or short.

Lévy Matters I

Author : Thomas Duquesne
Publisher : Springer Science & Business Media
ISBN 13 : 3642140068
Total Pages : 216 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Lévy Matters I by : Thomas Duquesne

Download or read book Lévy Matters I written by Thomas Duquesne and published by Springer Science & Business Media. This book was released on 2010-09-05 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.

Computational Methods for Option Pricing

Author : Yves Achdou
Publisher : SIAM
ISBN 13 : 9780898717495
Total Pages : 315 pages
Book Rating : 4.7/5 (174 download)

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Book Synopsis Computational Methods for Option Pricing by : Yves Achdou

Download or read book Computational Methods for Option Pricing written by Yves Achdou and published by SIAM. This book was released on 2005-01-01 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors review some important aspects of finance modeling involving partial differential equations and focus on numerical algorithms for the fast and accurate pricing of financial derivatives and for the calibration of parameters. This book explores the best numerical algorithms and discusses them in depth, from their mathematical analysis up to their implementation in C++ with efficient numerical libraries.

Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery

Author : Ning Xiong
Publisher : Springer Nature
ISBN 13 : 3031207386
Total Pages : 1527 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery by : Ning Xiong

Download or read book Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery written by Ning Xiong and published by Springer Nature. This book was released on 2023-01-29 with total page 1527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of papers on the recent progresses in the state of the art in natural computation, fuzzy systems, and knowledge discovery. The book is useful for researchers, including professors, graduate students, as well as R & D staff in the industry, with a general interest in natural computation, fuzzy systems, and knowledge discovery. The work printed in this book was presented at the 2022 18th International Conference on Natural Computation, Fuzzy Systems, and Knowledge Discovery (ICNC-FSKD 2022), held from 30 July to 1 August 2022, in Fuzhou, China. All papers were rigorously peer-reviewed by experts in the areas.

The Heston Model and Its Extensions in VBA

Author : Fabrice D. Rouah
Publisher : John Wiley & Sons
ISBN 13 : 1119003318
Total Pages : 359 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis The Heston Model and Its Extensions in VBA by : Fabrice D. Rouah

Download or read book The Heston Model and Its Extensions in VBA written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2015-03-24 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: Practical options pricing for better-informed investment decisions. The Heston Model and Its Extensions in VBA is the definitive guide to options pricing using two of the derivatives industry's most powerful modeling tools—the Heston model, and VBA. Light on theory, this extremely useful reference focuses on implementation, and can help investors more efficiently—and accurately—exploit market information to better inform investment decisions. Coverage includes a description of the Heston model, with specific emphasis on equity options pricing and variance modeling, The book focuses not only on the original Heston model, but also on the many enhancements and refinements that have been applied to the model, including methods that use the Fourier transform, numerical integration schemes, simulation, methods for pricing American options, and much more. The companion website offers pricing code in VBA that resides in an extensive set of Excel spreadsheets. The Heston model is the derivatives industry's most popular stochastic volatility model for pricing equity derivatives. This book provides complete guidance toward the successful implementation of this valuable model using the industry's ubiquitous financial modeling software, giving users the understanding—and VBA code—they need to produce option prices that are more accurate, and volatility surfaces that more closely reflect market conditions. Derivatives pricing is often the hinge on which profit is made or lost in financial institutions, making accuracy of utmost importance. This book will help risk managers, traders, portfolio managers, quants, academics and other professionals better understand the Heston model and its extensions, in a writing style that is clear, concise, transparent and easy to understand. For better pricing accuracy, The Heston Model and Its Extensions in VBA is a crucial resource for producing more accurate model outputs such as prices, hedge ratios, volatilities, and graphs.

Commodities

Author : M. A. H. Dempster
Publisher : CRC Press
ISBN 13 : 1498712339
Total Pages : 725 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Commodities by : M. A. H. Dempster

Download or read book Commodities written by M. A. H. Dempster and published by CRC Press. This book was released on 2015-11-05 with total page 725 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since a major source of income for many countries comes from exporting commodities, price discovery and information transmission between commodity futures markets are key issues for continued economic development.This book covers the fundamental theory of and derivatives pricing for major commodity markets as well as the interaction between commodi

The Oxford Handbook of Credit Derivatives

Author : Alexander Lipton
Publisher : Oxford University Press
ISBN 13 : 0199546789
Total Pages : 704 pages
Book Rating : 4.1/5 (995 download)

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Book Synopsis The Oxford Handbook of Credit Derivatives by : Alexander Lipton

Download or read book The Oxford Handbook of Credit Derivatives written by Alexander Lipton and published by Oxford University Press. This book was released on 2011-01-27 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a timely discussion of the mathematical modelling that underpins both credit derivatives and securitisation. It covers statistical analysis and techniques, modelling of default of both single and multiple entities, counterparty risk, Gaussian and non-Gaussian modelling, and securitisation.

Employee Stock Options: Exercise Timing, Hedging, And Valuation

Author : Tim Siu-tang Leung
Publisher : World Scientific
ISBN 13 : 9813209658
Total Pages : 228 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Employee Stock Options: Exercise Timing, Hedging, And Valuation by : Tim Siu-tang Leung

Download or read book Employee Stock Options: Exercise Timing, Hedging, And Valuation written by Tim Siu-tang Leung and published by World Scientific. This book was released on 2021-07-29 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Employee stock options (ESOs) are an integral component of compensation in the US. In fact, almost all S&P 500 companies grant options to their top executives, and the total value accounts for almost half of the total pay for their CEOs. In view of the extensive use and significant cost of ESOs to firms, the Financial Accounting Standards Board (FASB) has mandated expensing ESOs since 2004. This gives rise to the need to create a reasonable valuation method for these options for most firms that grant ESOs to their employees. The valuation of ESOs involves a number of challenging issues, and is thus an important active research area in Accounting, Corporate Finance, and Financial Mathematics.In this exciting book, the author discusses the practical and challenging problems surrounding ESOs from a financial mathematician's perspective. This book provides a systematic overview of the contractual features of ESOs and thoughtful discussions of different valuation approaches, with emphasis on three major aspects: (i) hedging strategies; (ii) exercise timing; and (iii) valuation methodologies. In addition to addressing each of these categories, this book also highlights their connections and combined effects of the cost of ESOs to firms, as well as examines the implications to modeling and valuation approaches. The book features a unique approach that combines stochastic modeling and control techniques with option pricing theory, and provides formulas and numerical schemes for fast implementation and clear illustration.

Leveraged Exchange-Traded Funds

Author : Tim Leung
Publisher : Springer
ISBN 13 : 3319290940
Total Pages : 104 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Leveraged Exchange-Traded Funds by : Tim Leung

Download or read book Leveraged Exchange-Traded Funds written by Tim Leung and published by Springer. This book was released on 2016-02-24 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an analysis, under both discrete-time and continuous-time frameworks, on the price dynamics of leveraged exchange-traded funds (LETFs), with emphasis on the roles of leverage ratio, realized volatility, investment horizon, and tracking errors. This study provides new insights on the risks associated with LETFs. It also leads to the discussion of new risk management concepts, such as admissible leverage ratios and admissible risk horizon, as well as the mathematical and empirical analyses of several trading strategies, including static portfolios, pairs trading, and stop-loss strategies involving ETFs and LETFs. The final part of the book addresses the pricing of options written on LETFs. Since different LETFs are designed to track the same reference index, these funds and their associated options share very similar sources of randomness. The authors provide a no-arbitrage pricing approach that consistently value options on LETFs with different leverage ratios with stochastic volatility and jumps in the reference index. Their results are useful for market making of these options, and for identifying price discrepancies across the LETF options markets. As the market of leveraged exchange-traded products become a sizeable connected part of the financial market, it is crucial to better understand its feedback effect and broader market impact. This is important not only for individual and institutional investors, but also for regulators.

The Heston Model and its Extensions in Matlab and C#

Author : Fabrice D. Rouah
Publisher : John Wiley & Sons
ISBN 13 : 1118695178
Total Pages : 437 pages
Book Rating : 4.1/5 (186 download)

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Book Synopsis The Heston Model and its Extensions in Matlab and C# by : Fabrice D. Rouah

Download or read book The Heston Model and its Extensions in Matlab and C# written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2013-08-01 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tap into the power of the most popular stochastic volatility model for pricing equity derivatives Since its introduction in 1993, the Heston model has become a popular model for pricing equity derivatives, and the most popular stochastic volatility model in financial engineering. This vital resource provides a thorough derivation of the original model, and includes the most important extensions and refinements that have allowed the model to produce option prices that are more accurate and volatility surfaces that better reflect market conditions. The book's material is drawn from research papers and many of the models covered and the computer codes are unavailable from other sources. The book is light on theory and instead highlights the implementation of the models. All of the models found here have been coded in Matlab and C#. This reliable resource offers an understanding of how the original model was derived from Ricatti equations, and shows how to implement implied and local volatility, Fourier methods applied to the model, numerical integration schemes, parameter estimation, simulation schemes, American options, the Heston model with time-dependent parameters, finite difference methods for the Heston PDE, the Greeks, and the double Heston model. A groundbreaking book dedicated to the exploration of the Heston model—a popular model for pricing equity derivatives Includes a companion website, which explores the Heston model and its extensions all coded in Matlab and C# Written by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management Engaging and informative, this is the first book to deal exclusively with the Heston Model and includes code in Matlab and C# for pricing under the model, as well as code for parameter estimation, simulation, finite difference methods, American options, and more.