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Analytic Methods For Pricing Double Barrier Options In The Presence Of Stochastic Volatility
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Book Synopsis Analytic Methods for Pricing Double Barrier Options in the Presence of Stochastic Volatility by : Oliver Faulhaber
Download or read book Analytic Methods for Pricing Double Barrier Options in the Presence of Stochastic Volatility written by Oliver Faulhaber and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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:
Book Synopsis Finite Difference Methods in Financial Engineering by : Daniel J. Duffy
Download or read book Finite Difference Methods in Financial Engineering written by Daniel J. Duffy and published by John Wiley & Sons. This book was released on 2013-10-28 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options Early exercise features and approximation using front-fixing, penalty and variational methods Modelling stochastic volatility models using Splitting methods Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work Modelling jumps using Partial Integro Differential Equations (PIDE) Free and moving boundary value problems in QF Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.
Book Synopsis On the Valuation of Fader and Discrete Barrier Options in Heston's Stochastic Volatility Model by : Susanne Griebsch
Download or read book On the Valuation of Fader and Discrete Barrier Options in Heston's Stochastic Volatility Model written by Susanne Griebsch and published by . This book was released on 2010 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: We focus on closed-form option pricing in Heston's stochastic volatility model, where closed-form formulas exist only for a few option types. Most of these closed-form solutions are constructed from characteristic functions. We follow this closed-form approach and derive multivariate characteristic functions depending on at least two spot values for different points in time. The derived characteristic functions are used as building blocks to set up (semi-) analytical pricing formulas for exotic options with payoffs depending on finitely many spot values such as fader options and discretely monitored barrier options. We compare our result with different numerical methods and examine accuracy and computational times.
Book Synopsis Pricing Window Barrier Options with a Hybrid Stochastic-Local Volatility Model by : Yu Tian
Download or read book Pricing Window Barrier Options with a Hybrid Stochastic-Local Volatility Model written by Yu Tian and published by . This book was released on 2014 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we present our research on pricing window barrier options under a hybrid stochastic-local volatility (SLV) model in the foreign exchange (FX) market. Due to the hybrid effect of the local volatility and stochastic volatility components of the model, the SLV model can reproduce the market implied volatility surface, and can improve the pricing accuracy for exotic options at the same time. In this paper, numerical techniques such as Monte Carlo and finite difference methods for standard exotic barrier options under the SLV model are extended to pricing window barrier options and numerical results produced by the SLV model are used to examine the performance and accuracy of the model for pricing window barrier options.
Book Synopsis Numerical Analysis Of Stochastic Volatility Jump Diffusion Models by : Abdelilah Jraifi
Download or read book Numerical Analysis Of Stochastic Volatility Jump Diffusion Models written by Abdelilah Jraifi and published by LAP Lambert Academic Publishing. This book was released on 2014-06-30 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the modern economic world, the options contracts are used because they allow to hedge against the vagaries and risks refers to fluctuations in the prices of the underlying assets. The determination of the price of these contracts is of great importance for investors.We are interested in problems of options pricing, actually the European and Quanto options on a financial asset. The price of that asset is modeled by a multi-dimentional jump diffusion with stochastic volatility. Otherwise, the first model considers the volatility as a continuous process and the second model considers it as a jump process. Finally in the 3rd model, the underlying asset is without jump and volatility follows a model CEV without jump. This model allow better to take into account some phenomena observed in the markets. We develop numerical methods that determine the values of prices for these options. We first write the model as an integro-differential stochastic equations system "EIDS," of which we study existence and unicity of solutions. Then we relate the resolution of PIDE to the computation of the option value.
Book Synopsis Robust Static Super-Replication of Barrier Options by : Jan H. Maruhn
Download or read book Robust Static Super-Replication of Barrier Options written by Jan H. Maruhn and published by Walter de Gruyter. This book was released on 2009-07-14 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Static hedge portfolios for barrier options are very sensitive with respect to changes of the volatility surface. To prevent potentially significant hedging losses this book develops a static super-replication strategy with market-typical robustness against volatility, skew and liquidity risk as well as model errors. Empirical results and various numerical examples confirm that the static superhedge successfully eliminates the risk of a changing volatility surface. Combined with associated sub-replication strategies this leads to robust price bounds for barrier options which are also relevant in the context of dynamic hedging. The mathematical techniques used to prove appropriate existence, duality and convergence results range from financial mathematics, stochastic and semi-infinite optimization, convex analysis and partial differential equations to semidefinite programming.
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 Pricing Path Dependent Contracts in the Presence of Stochastic Volatility - Combining Numerical Integration, Finite Difference and Conditional Monte Carlo by : William A. McGhee
Download or read book Pricing Path Dependent Contracts in the Presence of Stochastic Volatility - Combining Numerical Integration, Finite Difference and Conditional Monte Carlo written by William A. McGhee and published by . This book was released on 2014 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article the pricing of path dependent contracts combining conditional Monte Carlo, finite difference and numerical integration is considered. It will be shown that for two standard barrier contracts - one touch and knockout barrier options - very few Monte Carlo volatility paths, when combined with the other numerical methods, are required in order to accurately price these contracts in the presence of correlated stochastic volatility.
Book Synopsis Long Range Stochastic Volatility with Two Scales in Option Pricing by : Li Kong
Download or read book Long Range Stochastic Volatility with Two Scales in Option Pricing written by Li Kong and published by . This book was released on 2012 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: We exploit a general framework, a martingale approach method, to estimate the derivative price for different stochastic volatility models. This method is a very useful tool for handling non-markovian volatility models. With this method, we get the order of the approximation error by evaluating the orders of three error correction terms. We also summarize some challenges in using the martingale approach method to evaluate the derivative prices. We propose two stochastic volatility models. Our goal is to get the analytical solution for the derivative prices implied by the models. Another goal is to obtain an explicit model for the implied volatility and in particular how it depends on time to maturity. The first model we propose involves the increments of a standard Brownian Motion for a short time increment. The second model involves fractional Brownian Motion(fBm) and two scales. By using fBm in our model, we naturally incorporate a long-range dependence feature of the volatility process. In addition, the implied volatility corresponding to our second model capture a feature of the volatility as observed in the paper Maturity cycles in implied volatility by Fouque, which analyzed the S & P 500 option price data and observed that for long dated options the implied volatility is approximately affine in the reciprocal of time to maturity, while for short dated options the implied volatility is approximately affine in the reciprocal of square root of time to maturity. The leading term in the implied volatility also matches the case when we have time-dependent volatility in the Black-Scholes equation.
Book Synopsis A Semi-Group Expansion for Pricing Barrier Options by : Takashi Kato
Download or read book A Semi-Group Expansion for Pricing Barrier Options written by Takashi Kato and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a rigorous asymptotic expansion method with its numerical scheme for the Cauchy-Dirichlet problem in second order parabolic partial differential equations (PDEs). As an application, we propose a new approximation formula for pricing barrier option in the log-normal SABR stochastic volatility model.
Author :Antoine Petrus Cornelius van der Ploeg Publisher :Rozenberg Publishers ISBN 13 :9051705778 Total Pages :358 pages Book Rating :4.0/5 (517 download)
Book Synopsis Stochastic volatility and the pricing of financial derivatives by : Antoine Petrus Cornelius van der Ploeg
Download or read book Stochastic volatility and the pricing of financial derivatives written by Antoine Petrus Cornelius van der Ploeg and published by Rozenberg Publishers. This book was released on 2006 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Barrier Options Pricing in the Heston Stochastic Volatility Model by : Vitalija Alisauskaite
Download or read book Barrier Options Pricing in the Heston Stochastic Volatility Model written by Vitalija Alisauskaite and published by . This book was released on 2010 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models by : Jean-Pierre Fouque
Download or read book Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models written by Jean-Pierre Fouque and published by . This book was released on 2015 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of European and path-dependent options in a fast mean-reverting stochastic volatility setting. Our method is shown to be equivalent to those developed in Fouque, Papanicolaou, and Sircar (2000), but has the advantage of being able to price options for which the methods of Fouque et.al. are unsuitable. In particular, we are able to price double-barrier options. To our knowledge, this is the first time that double-barrier options have been priced in a stochastic volatility setting in which the Brownian motions driving the stock and volatility are correlated.
Book Synopsis Stochastic Dominance Option Pricing by : Stylianos Perrakis
Download or read book Stochastic Dominance Option Pricing written by Stylianos Perrakis and published by Springer. This book was released on 2019-05-03 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates the application of the economic concept of stochastic dominance to option markets and presents an alternative option pricing paradigm to the prevailing no arbitrage simultaneous equilibrium in the frictionless underlying and option markets. This new methodology was developed primarily by the author, working independently or jointly with other co-authors, over the course of more than thirty years. Among others, it yields the fundamental Black-Scholes-Merton option value when markets are complete, presents a new approach to the pricing of rare event risk, and uncovers option mispricing that leads to tradeable strategies in the presence of transaction costs. In the latter case it shows how a utility-maximizing investor trading in the market and a riskless bond, subject to proportional transaction costs, can increase his/her expected utility by overlaying a zero-net-cost portfolio of options bought at their ask price and written at their bid price, irrespective of the specific form of the utility function. The book contains a unified presentation of these methods and results, making it a highly readable supplement for educators and sophisticated professionals working in the popular field of option pricing. It also features a foreword by George Constantinides, the Leo Melamed Professor of Finance at the Booth School of Business, University of Chicago, USA, who was a co-author in several parts of the book.
Book Synopsis The Black-Scholes and Beyond Interactive Toolkit by : Neil Chriss
Download or read book The Black-Scholes and Beyond Interactive Toolkit written by Neil Chriss and published by McGraw-Hill Companies. This book was released on 1997 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces implied volatility trees as a new technique for pricing options, and provides a software package that should be comprehensible to anyone with experience or training in such pricing from other sources than this text. The text explains such aspects as probability theory, lumpy dividends, options on futures, hedge parameters for European options, implied volatility, and price barrier options in the presence of the smile. The software, on 3.5" disks, requires Windows 3.1 or 95, at least a 386 computer, a math coprocessor chip, and at least 8MB of RAM. No index or bibliography. Annotation copyrighted by Book News, Inc., Portland, OR
