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Author : Alessandro Sbuelz
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (535 download)
Download or read book Analytic American Option Pricing and Applications written by Alessandro Sbuelz and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alessandro Sbuelz
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)
Download or read book Analytic American Option Pricing written by Alessandro Sbuelz and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In a Black and Scholes (1973) world I study the pricing performance of a closed-form lower bound to American option values based on an exercise strategy corresponding to a flat exercise boundary. The lower bound has a simple two-step implementation akin to the Barone-Adesi and Whaley (1987) formula and shows superior pricing performance in the Out-of-The-Money region and for long maturities.
Author : Carl Chiarella
Publisher : World Scientific
ISBN 13 : 9814452629
Total Pages : 223 pages
Book Rating : 4.8/5 (144 download)
Download or read book The Numerical Solution of the American Option Pricing Problem written by Carl Chiarella and published by World Scientific. This book was released on 2014-10-14 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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"
Author : Alexandre C. Ziegler
Publisher : Springer Science & Business Media
ISBN 13 : 9783540206682
Total Pages : 200 pages
Book Rating : 4.2/5 (66 download)
Download or read book A Game Theory Analysis of Options written by Alexandre C. Ziegler and published by Springer Science & Business Media. This book was released on 2004-03-15 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern option pricing theory was developed in the late sixties and early seventies by F. Black, R. e. Merton and M. Scholes as an analytical tool for pricing and hedging option contracts and over-the-counter warrants. How ever, already in the seminal paper by Black and Scholes, the applicability of the model was regarded as much broader. In the second part of their paper, the authors demonstrated that a levered firm's equity can be regarded as an option on the value of the firm, and thus can be priced by option valuation techniques. A year later, Merton showed how the default risk structure of cor porate bonds can be determined by option pricing techniques. Option pricing models are now used to price virtually the full range of financial instruments and financial guarantees such as deposit insurance and collateral, and to quantify the associated risks. Over the years, option pricing has evolved from a set of specific models to a general analytical framework for analyzing the production process of financial contracts and their function in the financial intermediation process in a continuous time framework. However, very few attempts have been made in the literature to integrate game theory aspects, i. e. strategic financial decisions of the agents, into the continuous time framework. This is the unique contribution of the thesis of Dr. Alexandre Ziegler. Benefiting from the analytical tractability of contin uous time models and the closed form valuation models for derivatives, Dr.
Author : Chie-Bein Chen
Publisher :
ISBN 13 :
Total Pages : 12 pages
Book Rating : 4.:/5 (129 download)
Download or read book Analytical Pricing American Call Option with Dividend written by Chie-Bein Chen and published by . This book was released on 2008 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: American options provide early exercise opportunities to pose the additional difficulty to obtain the closed-form solution. In this study, a recursive formula is developed for determining the optimal exercise price of American call options with dividend based on the backward dynamic programming recursions and the Black-Scholes model combined with the Martingale pricing and the Girsanov Theorem. This recursive formula can be applied to two kinds of American call option pricing methods. One is analytical (closed-form) solution method, and the other is numerically analytical solution method. Numerically analytical solution method is an approach using the recursive formula through backward iterations only so that it is unable to obtain a general closed-form solution of America call option. The other one applies the backward recursive formula and the Taylor Series expansion to determine a general closed-form solution of the American call option.
Author : Lishang Jiang
Publisher : World Scientific Publishing Company
ISBN 13 : 9813106557
Total Pages : 343 pages
Book Rating : 4.8/5 (131 download)
Download or read book Mathematical Modeling And Methods Of Option Pricing written by Lishang Jiang and published by World Scientific Publishing Company. This book was released on 2005-07-18 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black-Scholes-Merton's option pricing theory.A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.
Author : Lishang Jiang
Publisher : World Scientific
ISBN 13 : 9812563695
Total Pages : 344 pages
Book Rating : 4.8/5 (125 download)
Download or read book Mathematical Modeling and Methods of Option Pricing written by Lishang Jiang and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.
Author : Carl Chiarella
Publisher : World Scientific
ISBN 13 : 9814452637
Total Pages : 223 pages
Book Rating : 4.8/5 (144 download)
Download or read book Numerical Solution Of The American Option Pricing Problem, The: Finite Difference And Transform Approaches written by Carl Chiarella and published by World Scientific. This book was released on 2014-10-14 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Andreas Andrikopoulos
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (129 download)
Download or read book Analytical Approximations to the Valuation of American Options written by Andreas Andrikopoulos and published by . This book was released on 2007 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quadratic approximation to the valuation of american options on stocks is revisited, constructing a pricing approach based on the fact that the early exercise policy should be chosen to maximize the value of the option. At the first part of the paper, we apply this approach (boundary-optimality) in the setting of the pricing model suggested in Barone-Adesi and Whaley (1987). We enrich their original valuation setting with an additional parameter, computed with the help of a boundary-optimality boundary condition. This approach enhances the accuracy performance of the Barone-Adesi and Whaley (1987) approximation. In the second part of the paper we introduce a novel approximation approach, where option value is the product of two functions, one of the being a function of time and the other one being a function of the stock price. Applying the principle that the early exercise policy should maximize option value, this alternative option pricing technique provides accurate results for american call and put options.
Author : In-Moo Kim
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)
Download or read book An Alternative Approach to the Valuation of American Options and Applications written by In-Moo Kim and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we examine the structure of American option valuation problems and derive analytic valuation formulas under general underlying security price processes by an alternative but intuitive method. For alternative diffusion processes, we derive quot;closed formquot; analytic valuation formulas and analyze the implications of asset price dynamics on the early exercise premiums of American options. In this regard, we introduce useful and interesting diffusion processes into American option pricing literature, thus providing a wide range of choices of pricing models for various American-type derivative assets. This work offers a useful analytic framework for future empirical testing and practical applications.
Author : Yves Hilpisch
Publisher : John Wiley & Sons
ISBN 13 : 1119037999
Total Pages : 390 pages
Book Rating : 4.1/5 (19 download)
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.
Author : Jerome Detemple
Publisher : CRC Press
ISBN 13 : 1420034863
Total Pages : 247 pages
Book Rating : 4.4/5 (2 download)
Download or read book American-Style Derivatives written by Jerome Detemple and published by CRC Press. This book was released on 2005-12-09 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on recent developments in the field, American-Style Derivatives provides an extensive treatment of option pricing with emphasis on the valuation of American options on dividend-paying assets. This book reviews valuation principles for European contingent claims and extends the analysis to American contingent claims. It presents basic valuation principles for American options including barrier, capped, and multi-asset options. It also reviews numerical methods for option pricing and compares their relative performance. Ideal for students and researchers in quantitative finance, this material is accessible to those with a background in stochastic processes or derivative securities.
Author : Donna Salopek
Publisher : CRC Press
ISBN 13 : 9780582315945
Total Pages : 132 pages
Book Rating : 4.3/5 (159 download)
Download or read book American Put Options written by Donna Salopek and published by CRC Press. This book was released on 1997-03-15 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: An American put option gives its owner the right to sell a share of stock at a given specified price on or before a given date. This book provides a detailed comparison of recent works on the American put option from both theoretical and computational approaches.
Author : Timothy Falcon Crack
Publisher :
ISBN 13 : 9780995117396
Total Pages : 284 pages
Book Rating : 4.1/5 (173 download)
Download or read book Basic Black-Scholes written by Timothy Falcon Crack and published by . This book was released on 2021-04 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: [Note: eBook now available; see Amazon author page for details.] THE AUTHOR: Dr. Crack studied PhD-level option pricing at MIT and Harvard Business School, taught undergrad and MBA option pricing at Indiana University (winning many teaching awards), was an independent consultant to the New York Stock Exchange, worked as an asset management practitioner in London, and has traded options for over 20 years. This unique mix of learning, teaching, consulting, practice, and trading is reflected in every page. This revised 5th edition gives clear explanations of Black-Scholes option pricing theory, and discusses direct applications of the theory to trading. The presentation does not go far beyond basic Black-Scholes for three reasons: First, a novice need not go far beyond Black-Scholes to make money in the options markets; Second, all high-level option pricing theory is simply an extension of Black-Scholes; and Third, there already exist many books that look far beyond Black-Scholes without first laying the firm foundation given here. The trading advice does not go far beyond elementary call and put positions because more complex trades are simply combinations of these. UNIQUE SELLING POINTS -The basic intuition you need to trade options for the first time, or interview for an options job. -Honest advice about trading: there is no simple way to beat the markets, but if you have skill this advice can help make you money, and if you have no skill but still choose to trade, this advice can reduce your losses. -Full immersion treatment of transactions costs (T-costs). -Lessons from trading stated in simple terms. -Stylized facts about the markets (e.g., how to profit from reversals, when are T-costs highest/lowest during the trading day, implications of the market for corporate control, etc.). -How to apply European-style Black-Scholes pricing to the trading of American-style options. -Leverage through margin trading compared to leverage through options, including worked spreadsheet example. -Black-Scholes pricing code for the HP17B, HP19B, and HP12C. -Three downloadable spreadsheets. One allows the user to forecast T-costs for option positions using simple models. Another allows the user to explore option sensitivities including the Greeks. -Practitioner Bloomberg Terminal screenshots to aid learning. -Simple discussion of continuously-compounded returns. -Introduction to "paratrading" (trading stocks side-by-side with options to generate additional profit). -Unique "regrets" treatment of early exercise decisions and trade-offs for American-style calls and puts. -Unique discussion of put-call parity and option pricing. -How to calculate Black-Scholes in your head in 10 seconds (also in Heard on The Street: Quantitative Questions from Wall Street Job Interviews). -Special attention to arithmetic Brownian motion with general pricing formulae and comparisons to Bachelier (1900) and Black-Scholes. -Careful attention to the impact of dividends in analytical American option pricing. -Dimensional analysis and the adequation formula (relating FX call and FX put prices through transformed Black-Scholes formulae). -Intuitive review of risk-neutral pricing/probabilities and how and why these are related to physical pricing/probabilities. -Careful distinction between the early Merton (non-risk-neutral) hedging-type argument and later Cox-Ross/Harrison-Kreps risk-neutral pricing -Simple discussion of Monte-Carlo methods in science and option pricing. -Simple interpretations of the Black-Scholes formula and PDE and implications for trading. -Careful discussion of conditional probabilities as they relate to Black-Scholes. -Intuitive treatment of high-level topics e.g., bond-numeraire interpretation of Black-Scholes (where N(d2) is P(ITM)) versus the stock-numeraire interpretation (where N(d1) is P(ITM)). -Introduction and discussion of the risk-neutral probability that a European-style call or put option is ever in the money during its life.
Author : Julien Guyon
Publisher : CRC Press
ISBN 13 : 1466570342
Total Pages : 480 pages
Book Rating : 4.4/5 (665 download)
Download or read book Nonlinear Option Pricing written by Julien Guyon and published by CRC Press. This book was released on 2013-12-19 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: New Tools to Solve Your Option Pricing ProblemsFor nonlinear PDEs encountered in quantitative finance, advanced probabilistic methods are needed to address dimensionality issues. Written by two leaders in quantitative research-including Risk magazine's 2013 Quant of the Year-Nonlinear Option Pricing compares various numerical methods for solving hi
Author : Alexander Izmailov
Publisher :
ISBN 13 :
Total Pages : 17 pages
Book Rating : 4.:/5 (13 download)
Download or read book Complete Analytical Solution of the American Style Option Pricing with Constant and Stochastic Volatilities written by Alexander Izmailov and published by . This book was released on 2015 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first ever explicit formulation of the concept of an option's probability density functions has been introduced in our publications “Breakthrough in Understanding Derivatives and Option Based Hedging - Marginal and Joint Probability Density Functions of Vanilla Options - True Value-at-Risk and Option Based Hedging Strategies”, “Complete Analytical Solution of the Asian Option Pricing and Asian Option Value-at-Risk Problems. A Probability Density Function Approach” and “Complete Analytical Solution of the Heston Model for Option Pricing and Value-At-Risk Problems. A Probability Density Function Approach.” Please see links 'http://ssrn.com/abstract=2489601 ' http://ssrn.com/abstract= 2489601, 'http://ssrn.com/abstract=2546430 ' http://ssrn.com/abstract= 2546430, 'http://ssrn.com/abstract=2549033 ' http://ssrn.com/abstract= 2549033). In this paper we report unique analytical results for pricing American Style Options in the presence of both constant and stochastic volatility (Heston model), enabling complete analytical resolution of all problems associated with American Style Options considered within the Heston Model. Our discovery of the probability density function for American and European Style Options with constant and stochastic volatilities enables exact closed-form analytical results for their expected values (prices) for the first time without depending on approximate numerical methods. Option prices, i.e. their expected values, are just the first moments. All higher moments are as easily represented in closed form based on our probability density function, but are not calculable by extensions of other numerical methods now used to represent the first moment. Our formulation of the density functions for options with American and European Style execution rights with constant and stochastic volatility (Heston model) is expressive enough to enable derivation for the first time ever of corollary closed-form analytical results for such Value-At-Risk characteristics as the probabilities that options with different execution rights, with constant or stochastic volatility, will be below or above any set of thresholds at termination. Such assessments are absolutely out of reach of current published methods for treating options.All numerical evaluations based on our analytical results are practically instantaneous and absolutely accurate.
Author : S. Gounden
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
Download or read book An Analytic Formula for the Price of American Exchange Options written by S. Gounden and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article we demononstrate how to find an analytic solution to the pricing of American exchange options using homotogy methods. As an aside we derive formula for American call and put options when the underlying pays a continuous dividend. These solutions are given in terms of power series.
