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Option Pricing With Fourier Series
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Book Synopsis Option Pricing with Fourier Series by : Baye M. Dia
Download or read book Option Pricing with Fourier Series written by Baye M. Dia and published by . This book was released on 2009 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a simple and fairly general approach for valuing European options in closed-form. This approach leads to a single formula for the price of a European option. This formula is easy to implement, fast to execute, and only involves working with real numbers, in contrast to the Fourier transform based option pricing formulas. It also applies many option pricing models existing in the literature. Furthermore, the formula and the derived expressions of option quot;Greeksquot; are payoff as well as model independent, in the sense that their structure remains unchanged for any payoff and any pricing model, unlike existing pricing formulas.
Book Synopsis Modular Pricing of Options by : Jianwei Zhu
Download or read book Modular Pricing of Options written by Jianwei Zhu and published by Springer. This book was released on 2014-03-12 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: From a technical point of view, the celebrated Black and Scholes option pricing formula was originally developed using a separation of variables technique. However, already Merton mentioned in his seminal 1973 pa per, that it could have been developed by using Fourier transforms as well. Indeed, as is well known nowadays, Fourier transforms are a rather convenient solution technique for many models involving the fundamental partial differential equation of financial economics. It took the community nearly another twenty years to recognize that Fourier transform is even more useful, if one applies it to problems in financial economics without seeking an explicit analytical inverse trans form. Heston (1993) probably was the first to demonstrate how to solve a stochastic volatility option pricing model quasi analytically using the characteristic function of the problem, which is nothing else than the Fourier transform of the underlying Arrow /Debreu-prices, and doing the inverse transformation numerically. This opened the door for a whole bunch of new closed form solutions in the transformed Fourier space and still is one of the most active research areas in financial economics.
Book Synopsis Fourier Transform Methods in Finance by : Umberto Cherubini
Download or read book Fourier Transform Methods in Finance written by Umberto Cherubini and published by John Wiley & Sons. This book was released on 2010-01-05 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market quotes. Fourier Transform Methods in Finance is a practical and accessible guide to pricing financial instruments using Fourier transform. Written by an experienced team of practitioners and academics, it covers Fourier pricing methods; the dynamics of asset prices; non stationary market dynamics; arbitrage free pricing; generalized functions and the Fourier transform method. Readers will learn how to: compute the Hilbert transform of the pricing kernel under a Fast Fourier Transform (FFT) technique characterise the price dynamics on a market in terms of the characteristic function, allowing for both diffusive processes and jumps apply the concept of characteristic function to non-stationary processes, in particular in the presence of stochastic volatility and more generally time change techniques perform a change of measure on the characteristic function in order to make the price process a martingale recover a general representation of the pricing kernel of the economy in terms of Hilbert transform using the theory of generalised functions apply the pricing formula to the most famous pricing models, with stochastic volatility and jumps. Junior and senior practitioners alike will benefit from this quick reference guide to state of the art models and market calibration techniques. Not only will it enable them to write an algorithm for option pricing using the most advanced models, calibrate a pricing model on options data, and extract the implied probability distribution in market data, they will also understand the most advanced models and techniques and discover how these techniques have been adjusted for applications in finance. ISBN 978-0-470-99400-9
Book Synopsis Derivatives Analytics with Python by : Yves Hilpisch
Download or read book Derivatives Analytics with Python written by Yves Hilpisch and published by John Wiley & Sons. This book was released on 2015-08-03 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supercharge options analytics and hedging using the power of Python Derivatives Analytics with Python shows you how to implement market-consistent valuation and hedging approaches using advanced financial models, efficient numerical techniques, and the powerful capabilities of the Python programming language. This unique guide offers detailed explanations of all theory, methods, and processes, giving you the background and tools necessary to value stock index options from a sound foundation. You'll find and use self-contained Python scripts and modules and learn how to apply Python to advanced data and derivatives analytics as you benefit from the 5,000+ lines of code that are provided to help you reproduce the results and graphics presented. Coverage includes market data analysis, risk-neutral valuation, Monte Carlo simulation, model calibration, valuation, and dynamic hedging, with models that exhibit stochastic volatility, jump components, stochastic short rates, and more. The companion website features all code and IPython Notebooks for immediate execution and automation. Python is gaining ground in the derivatives analytics space, allowing institutions to quickly and efficiently deliver portfolio, trading, and risk management results. This book is the finance professional's guide to exploiting Python's capabilities for efficient and performing derivatives analytics. Reproduce major stylized facts of equity and options markets yourself Apply Fourier transform techniques and advanced Monte Carlo pricing Calibrate advanced option pricing models to market data Integrate advanced models and numeric methods to dynamically hedge options Recent developments in the Python ecosystem enable analysts to implement analytics tasks as performing as with C or C++, but using only about one-tenth of the code or even less. Derivatives Analytics with Python — Data Analysis, Models, Simulation, Calibration and Hedging shows you what you need to know to supercharge your derivatives and risk analytics efforts.
Book Synopsis Applications of Fourier Transform to Smile Modeling by : Jianwei Zhu
Download or read book Applications of Fourier Transform to Smile Modeling written by Jianwei Zhu and published by Springer Science & Business Media. This book was released on 2009-10-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the applications of Fourier transform to smile modeling. Smile effect is used generically by ?nancial engineers and risk managers to refer to the inconsistences of quoted implied volatilities in ?nancial markets, or more mat- matically, to the leptokurtic distributions of ?nancial assets and indices. Therefore, a sound modeling of smile effect is the central challenge in quantitative ?nance. Since more than one decade, Fourier transform has triggered a technical revolution in option pricing theory. Almost all new developed option pricing models, es- cially in connection with stochastic volatility and random jump, have extensively applied Fourier transform and the corresponding inverse transform to express - tion pricing formulas. The large accommodation of the Fourier transform allows for a very convenient modeling with a general class of stochastic processes and d- tributions. This book is then intended to present a comprehensive treatment of the Fourier transform in the option valuation, covering the most stochastic factors such as stochastic volatilities and interest rates, Poisson and Levy ́ jumps, including some asset classes such as equity, FX and interest rates, and providing numerical ex- ples and prototype programming codes. I hope that readers will bene?t from this book not only by gaining an overview of the advanced theory and the vast large l- erature on these topics, but also by gaining a ?rst-hand feedback from the practice on the applications and implementations of the theory.
Book Synopsis PDE and Martingale Methods in Option Pricing by : Andrea Pascucci
Download or read book PDE and Martingale Methods in Option Pricing written by Andrea Pascucci and published by Springer Science & Business Media. This book was released on 2011-04-15 with total page 727 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to the mathematical, probabilistic and numerical methods used in the modern theory of option pricing. The text is designed for readers with a basic mathematical background. The first part contains a presentation of the arbitrage theory in discrete time. In the second part, the theories of stochastic calculus and parabolic PDEs are developed in detail and the classical arbitrage theory is analyzed in a Markovian setting by means of of PDEs techniques. After the martingale representation theorems and the Girsanov theory have been presented, arbitrage pricing is revisited in the martingale theory optics. General tools from PDE and martingale theories are also used in the analysis of volatility modeling. The book also contains an Introduction to Lévy processes and Malliavin calculus. The last part is devoted to the description of the numerical methods used in option pricing: Monte Carlo, binomial trees, finite differences and Fourier transform.
Book Synopsis The Fourier Transform Method in Option Pricing by : Yannan Gao
Download or read book The Fourier Transform Method in Option Pricing written by Yannan Gao and published by . This book was released on 2014 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Exotic Option Pricing and Advanced Lévy Models by : Andreas Kyprianou
Download or read book Exotic Option Pricing and Advanced Lévy Models written by Andreas Kyprianou and published by John Wiley & Sons. This book was released on 2006-06-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Lévy process. Working with Lévy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Lévy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Lévy markets, written by leading scientists in this field. In recent years, Lévy processes have leapt to the fore as a tractable mechanism for modeling asset returns. Exotic option values are especially sensitive to an accurate portrayal of these dynamics. This comprehensive volume provides a valuable service for financial researchers everywhere by assembling key contributions from the world's leading researchers in the field. Peter Carr, Head of Quantitative Finance, Bloomberg LP. This book provides a front-row seat to the hottest new field in modern finance: options pricing in turbulent markets. The old models have failed, as many a professional investor can sadly attest. So many of the brightest minds in mathematical finance across the globe are now in search of new, more accurate models. Here, in one volume, is a comprehensive selection of this cutting-edge research. Richard L. Hudson, former Managing Editor of The Wall Street Journal Europe, and co-author with Benoit B. Mandelbrot of The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward
Book Synopsis Mathematical Modeling And Computation In Finance: With Exercises And Python And Matlab Computer Codes by : Cornelis W Oosterlee
Download or read book Mathematical Modeling And Computation In Finance: With Exercises And Python And Matlab Computer Codes written by Cornelis W Oosterlee and published by World Scientific. This book was released on 2019-10-29 with total page 1310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance.When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, 'do not fall in love with your favorite model.' The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing.The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.Supplementary Material:Solutions Manual is available to instructors who adopt this textbook for their courses. Please contact [email protected].
Book Synopsis Applications of the Fast Fourier Transform in Option Pricing by : Elaine Cunningham
Download or read book Applications of the Fast Fourier Transform in Option Pricing written by Elaine Cunningham and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Option Pricing with Stochastic Volatility by : Bogdan Negrea
Download or read book Option Pricing with Stochastic Volatility written by Bogdan Negrea and published by . This book was released on 2002 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Black and Scholes (1973) option pricing model was developed starting from the hypothesis of constant volatility. However, many empirical studies, have argued that the mentioned hypothesis is subject to debate. A few authors, among who - Stein and Stein (1991), Heston (1993), Bates (1996) and Bakshi et al.(1997, 2000) - suggested the use of the Fourier transform for the density of the underlying return or for the risk-neutral probabilities, in order to evaluate the fair price of an option. In this paper we propose a stochastic valuation model using the Fourier transform for option price. This model can be used for the valuation of European options, characterized by two state variables: the price of the underlying asset and its volatility. We model the stochastic processes described by the two variables and we obtain a partial derivatives equation of which the solution is the price of the derivative. We propose a solution to this partial derivatives equation using the Fourier transform. When we apply the Fourier transform, we demonstrate that a second order partial derivatives equation is solved as an ordinary differential equation. We consider a correlation between the underlying asset price and its volatility and two sources of risk: return and volatility. The first part of the paper describes the hypotheses of the model. After describing the Fourier transforms, we propose a formula for the valuation of European options with stochastic volatility. In the second part, we present a few empirical results on the pricing of CAC 40 index call options.
Book Synopsis Fast Fourier Transform and Option Pricing by : Aleš Černý
Download or read book Fast Fourier Transform and Option Pricing written by Aleš Černý and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article is a concise introduction to applications of Fourier transform and FFT in option pricing.
Book Synopsis Option Pricing Using Fourier Transform Under Affine Stochastic Volatility Models by : Lu Tian
Download or read book Option Pricing Using Fourier Transform Under Affine Stochastic Volatility Models written by Lu Tian and published by . This book was released on 2012 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Foreign Exchange Option Pricing by : Iain J. Clark
Download or read book Foreign Exchange Option Pricing written by Iain J. Clark and published by John Wiley & Sons. This book was released on 2011-01-18 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers foreign exchange options from the point of view of the finance practitioner. It contains everything a quant or trader working in a bank or hedge fund would need to know about the mathematics of foreign exchange—not just the theoretical mathematics covered in other books but also comprehensive coverage of implementation, pricing and calibration. With content developed with input from traders and with examples using real-world data, this book introduces many of the more commonly requested products from FX options trading desks, together with the models that capture the risk characteristics necessary to price these products accurately. Crucially, this book describes the numerical methods required for calibration of these models – an area often neglected in the literature, which is nevertheless of paramount importance in practice. Thorough treatment is given in one unified text to the following features: Correct market conventions for FX volatility surface construction Adjustment for settlement and delayed delivery of options Pricing of vanillas and barrier options under the volatility smile Barrier bending for limiting barrier discontinuity risk near expiry Industry strength partial differential equations in one and several spatial variables using finite differences on nonuniform grids Fourier transform methods for pricing European options using characteristic functions Stochastic and local volatility models, and a mixed stochastic/local volatility model Three-factor long-dated FX model Numerical calibration techniques for all the models in this work The augmented state variable approach for pricing strongly path-dependent options using either partial differential equations or Monte Carlo simulation Connecting mathematically rigorous theory with practice, this is the essential guide to foreign exchange options in the context of the real financial marketplace.
Book Synopsis Option Pricing Using Fourier Transform with a Focus on the Cosine Expansion by : Marek Kolman
Download or read book Option Pricing Using Fourier Transform with a Focus on the Cosine Expansion written by Marek Kolman and published by . This book was released on 2015 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: A selection of Fourier transform methodologies for option pricing is presented. The focus is aimed at the cosine method which is endowed with attractive properties. The methodologies are applied to a particularly selected pricing problem and also are compared against closed-form formulas if these are available. To thoroughly test these methods, we have chosen option data exhibiting a significant volatility smile which could rule out some of the methodologies if these are unable to capture the special properties of ITM or OTM options. It is shown that in some cases the transform approaches outperforms the closed-form formulas also in speed. In particular, the Fourier-cosine expansion is robust, general, very fast and therefore it seems to be an ideal candidate for implementation of option-pricing model even by the practitioners.
Book Synopsis Mathematical Finance - Bachelier Congress 2000 by : Helyette Geman
Download or read book Mathematical Finance - Bachelier Congress 2000 written by Helyette Geman and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Bachelier Society for Mathematical Finance held its first World Congress in Paris last year, and coincided with the centenary of Louis Bacheliers thesis defence. In his thesis Bachelier introduces Brownian motion as a tool for the analysis of financial markets as well as the exact definition of options. The thesis is viewed by many the key event that marked the emergence of mathematical finance as a scientific discipline. The prestigious list of plenary speakers in Paris included two Nobel laureates, Paul Samuelson and Robert Merton, and the mathematicians Henry McKean and S.R.S. Varadhan. Over 130 further selected talks were given in three parallel sessions. .
Book Synopsis Option Pricing Under the CGGMY-model by : Daniel Djurdjevic
Download or read book Option Pricing Under the CGGMY-model written by Daniel Djurdjevic and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
