Modular Pricing Of Options
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Modular Pricing Of Options
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Author : Jianwei Zhu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Modular Pricing Of Options written by Jianwei Zhu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Business & Economics categories.
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.
The Numerical Solution Of The American Option Pricing Problem
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Author : Carl Chiarella
language : en
Publisher: World Scientific
Release Date : 2014-10-14
The Numerical Solution Of The American Option Pricing Problem written by Carl Chiarella and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-14 with Options (Finance) categories.
The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical approaches that have proved useful for finding all prices, hedge ratios and early exercise boundaries of an American option. One is a finite difference approach which is based on the numerical solution of the partial differential equations with the free boundary problem arising in American option pricing, including the method of lines, the component wise splitting and the finite difference with PSOR. The other approach is the integral transform approach which includes Fourier or Fourier Cosine transforms. Written in a concise and systematic manner, Chiarella, Kang and Meyer explain and demonstrate the advantages and limitations of each of them based on their and their co-workers'' experiences with these approaches over the years. Contents: Introduction; The Merton and Heston Model for a Call; American Call Options under Jump-Diffusion Processes; American Option Prices under Stochastic Volatility and Jump-Diffusion Dynamics OCo The Transform Approach; Representation and Numerical Approximation of American Option Prices under Heston; Fourier Cosine Expansion Approach; A Numerical Approach to Pricing American Call Options under SVJD; Conclusion; Bibliography; Index; About the Authors. Readership: Post-graduates/ Researchers in finance and applied mathematics with interest in numerical methods for American option pricing; mathematicians/physicists doing applied research in option pricing. Key Features: Complete discussion of different numerical methods for American options; Able to handle stochastic volatility and/or jump diffusion dynamics; Able to produce hedge ratios efficiently and accurately"
Numerical Solution Of The American Option Pricing Problem The Finite Difference And Transform Approaches
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Author : Carl Chiarella
language : en
Publisher: World Scientific
Release Date : 2014-10-14
Numerical Solution Of The American Option Pricing Problem The Finite Difference And Transform Approaches written by Carl Chiarella and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-14 with Business & Economics categories.
The early exercise opportunity of an American option makes it challenging to price and an array of approaches have been proposed in the vast literature on this topic. In The Numerical Solution of the American Option Pricing Problem, Carl Chiarella, Boda Kang and Gunter Meyer focus on two numerical approaches that have proved useful for finding all prices, hedge ratios and early exercise boundaries of an American option. One is a finite difference approach which is based on the numerical solution of the partial differential equations with the free boundary problem arising in American option pricing, including the method of lines, the component wise splitting and the finite difference with PSOR. The other approach is the integral transform approach which includes Fourier or Fourier Cosine transforms. Written in a concise and systematic manner, Chiarella, Kang and Meyer explain and demonstrate the advantages and limitations of each of them based on their and their co-workers' experiences with these approaches over the years.
Foreign Exchange Option Pricing
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Author : Iain J. Clark
language : en
Publisher: John Wiley & Sons
Release Date : 2011-01-18
Foreign Exchange Option Pricing written by Iain J. Clark and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-18 with Business & Economics categories.
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.
American Type Options
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Author : Dmitrii S. Silvestrov
language : en
Publisher: Walter de Gruyter
Release Date : 2013-11-27
American Type Options written by Dmitrii S. Silvestrov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
The book gives a systematical presentation of stochastic approximation methods for models of American-type options with general pay-off functions for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The book also contains an extended bibliography of works in the area. This book is the first volume of the comprehensive two volumes monograph. The second volume will present results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.
Pricing In In Complete Markets
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Author : Angelika Esser
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-27
Pricing In In Complete Markets written by Angelika Esser and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-27 with Business & Economics categories.
In this book, the authors investigate structural aspects of no arbitrage pricing of contingent claims and applications of the general pricing theory in the context of incomplete markets. A quasi-closed form pricing equation in terms of artificial probabilities is derived for arbitrary payoff structures. Moreover, a comparison between continuous and discrete models is presented, highlighting the major similarities and key differences. As applications, two sources of market incompleteness are considered, namely stochastic volatility and stochastic liquidity. Firstly, the general theory discussed before is applied to the pricing of power options in a stochastic volatility model. Secondly, the issue of liquidity risk is considered by focusing on the aspect of how asset price dynamics are affected by the trading strategy of a large investor.
Pricing Interest Rate Derivatives
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Author : Markus Bouziane
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-18
Pricing Interest Rate Derivatives written by Markus Bouziane and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-03-18 with Business & Economics categories.
The author derives an efficient and accurate pricing tool for interest-rate derivatives within a Fourier-transform based pricing approach, which is generally applicable to exponential-affine jump-diffusion models.
Asset Pricing
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Author : B.Philipp Kellerhals
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-02
Asset Pricing written by B.Philipp Kellerhals and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-02 with Business & Economics categories.
The modern field of asset pricing asks for sound pricing models grounded on the theory of financial economies a la Ingersoll (1987) as weIl as for accu rate estimation techniques a la Hamilton (1994b) when it comes to empirical inferences of the specified model. The idea behind this book on hand is to provide the reader with a canonical framework that shows how to bridge the gap between the continuous-time pricing practice in financial engineering and the capital market data inevitably only available at discrete time intervals. Three major financial markets are to be examined for which we select the equity market, the bond market, and the electricity market. In each mar ket we derive new valuation models to price selected financial instruments in continuous-time. The decision criterium for choosing a continuous-time model ing framework is the richness of the stochastic theory available for continuous time processes with Merton's pioneering contributions to financial economics, collected in Merton (1992). The continuous-time framework, reviewed and as sessed by Sundaresan (2000), allows us to obtain analytical pricing formulae that would be unavailable in a discrete time setting. However, at the time of implementing the derived theoretical pricing models on market data, that is necessarily sampled at discrete time intervals, we work with so-called exact discrete time equivalents a la Bergstrom (1984). We show how to conveniently work within astate space framework which we derive in a general setting as weIl as explicitly for each of the three applications.
Asset Price Dynamics Volatility And Prediction
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Author : Stephen J. Taylor
language : en
Publisher: Princeton University Press
Release Date : 2011-02-11
Asset Price Dynamics Volatility And Prediction written by Stephen J. Taylor and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-11 with Business & Economics categories.
This book shows how current and recent market prices convey information about the probability distributions that govern future prices. Moving beyond purely theoretical models, Stephen Taylor applies methods supported by empirical research of equity and foreign exchange markets to show how daily and more frequent asset prices, and the prices of option contracts, can be used to construct and assess predictions about future prices, their volatility, and their probability distributions. Stephen Taylor provides a comprehensive introduction to the dynamic behavior of asset prices, relying on finance theory and statistical evidence. He uses stochastic processes to define mathematical models for price dynamics, but with less mathematics than in alternative texts. The key topics covered include random walk tests, trading rules, ARCH models, stochastic volatility models, high-frequency datasets, and the information that option prices imply about volatility and distributions. Asset Price Dynamics, Volatility, and Prediction is ideal for students of economics, finance, and mathematics who are studying financial econometrics, and will enable researchers to identify and apply appropriate models and methods. It will likewise be a valuable resource for quantitative analysts, fund managers, risk managers, and investors who seek realistic expectations about future asset prices and the risks to which they are exposed.
Applications Of Fourier Transform To Smile Modeling
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Author : Jianwei Zhu
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-03
Applications Of Fourier Transform To Smile Modeling written by Jianwei Zhu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-03 with Business & Economics categories.
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.