American Put Options With Regime Switching Volatility

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American Put Options with Regime-Switching Volatility

Author : Bong-Gyu Jang
Publisher :
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis American Put Options with Regime-Switching Volatility by : Bong-Gyu Jang

Download or read book American Put Options with Regime-Switching Volatility written by Bong-Gyu Jang and published by . This book was released on 2005 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we study the price of an American option with stochastic volatility. The nature of stochastic volatility in this paper is as follows: volatility can take two values and changes at the jump time of an independent Poisson process. Namely, the volatility of the underlying asset changes between two regimes, say 'high volatility regime' H and 'low volatility regime' L. We derive an analytic formula for the price of a perpetual put and prove that the price of the perpetual put is always higher in the high volatility regime than in the low volatility regime and the exercise boundary is lower in the high volatility regime than in the low volatility regime. We also show by numerical examples that the Richardson interpolation together with the randomization method by Carr (1998) provides a fast algorithm to approximate the price of an American put with finite expiry and compare our numerical results with the previous study by Bollen (1998).

Perpetual American Options in Regime-Switching Models

Author : Svetlana Boyarchenko
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Perpetual American Options in Regime-Switching Models by : Svetlana Boyarchenko

Download or read book Perpetual American Options in Regime-Switching Models written by Svetlana Boyarchenko and published by . This book was released on 2007 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the paper, we solve the pricing problem for perpetual American options in Markov-modulated Levy models. The early exercise boundaries and prices are calculated using an iteration procedure. The pricing procedure is efficient even if the number of states is large provided the transition rates are not large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modelled as finite-state Markov chains.

Perpetual American Vanilla Option Pricing Under Single Regime Change Risk - An Exhaustive Study

Author : Miquel Montero
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis Perpetual American Vanilla Option Pricing Under Single Regime Change Risk - An Exhaustive Study by : Miquel Montero

Download or read book Perpetual American Vanilla Option Pricing Under Single Regime Change Risk - An Exhaustive Study written by Miquel Montero and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in which some of the properties volatility and dividend policy of the underlying stock can change at a random instant of time, but in such a way that we can forecast their final values. Under this assumption we can model actual market conditions because most relevant facts usually entail sharp predictable consequences. The effect of this potential risk on perpetual American vanilla options is remarkable: the very equation that will determine the fair price depends on the solution to be found. Sound results are found under the optics both of finance and physics. In particular, a parallelism among the overall outcome of this problem and a phase transition is established.

American Put Options

Author : Donna Salopek
Publisher : CRC Press
ISBN 13 : 9780582315945
Total Pages : 132 pages
Book Rating : 4.3/5 (159 download)

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Book Synopsis American Put Options by : Donna Salopek

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.

Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities

Author : Anatoli? Vital?evich Svishchuk
Publisher : World Scientific
ISBN 13 : 9814440132
Total Pages : 326 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities by : Anatoli? Vital?evich Svishchuk

Download or read book Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities written by Anatoli? Vital?evich Svishchuk and published by World Scientific. This book was released on 2013 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities is devoted to the modeling and pricing of various kinds of swaps, such as those for variance, volatility, covariance, correlation, for financial and energy markets with different stochastic volatilities, which include CIR process, regime-switching, delayed, mean-reverting, multi-factor, fractional, Levy-based, semi-Markov and COGARCH(1,1). One of the main methods used in this book is change of time method. The book outlines how the change of time method works for different kinds of models and problems arising in financial and energy markets and the associated problems in modeling and pricing of a variety of swaps. The book also contains a study of a new model, the delayed Heston model, which improves the volatility surface fitting as compared with the classical Heston model. The author calculates variance and volatility swaps for this model and provides hedging techniques. The book considers content on the pricing of variance and volatility swaps and option pricing formula for mean-reverting models in energy markets. Some topics such as forward and futures in energy markets priced by multi-factor Levy models and generalization of Black-76 formula with Markov-modulated volatility are part of the book as well, and it includes many numerical examples such as S&P60 Canada Index, S&P500 Index and AECO Natural Gas Index.

American Options in Levy Models With Stochastic Interest Rate of CIR-Type

Author : Svetlana Boyarchenko
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)

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Book Synopsis American Options in Levy Models With Stochastic Interest Rate of CIR-Type by : Svetlana Boyarchenko

Download or read book American Options in Levy Models With Stochastic Interest Rate of CIR-Type written by Svetlana Boyarchenko and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general numerical method for pricing American options in regime switching jump diffusion models of stock dynamics with stochastic interest rates and/or volatility is developed. Time derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options in a Markov-modulated Levy model. Options in this sequence are solved using an iteration method based on the Wiener-Hopf factorization. As an application, an explicit algorithm for the case of interest rate driven by the square root process with embedded jumps is derived. Numerical examples show that fairly accurate results can be obtained in reasonable time. It is shown that the shape of the early exercise boundary strongly depends on the sign of the leverage parameter.

Stochastic Optimization

Author : Stanislav Uryasev
Publisher : Springer Science & Business Media
ISBN 13 : 1475765940
Total Pages : 438 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Stochastic Optimization by : Stanislav Uryasev

Download or read book Stochastic Optimization written by Stanislav Uryasev and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic programming is the study of procedures for decision making under the presence of uncertainties and risks. Stochastic programming approaches have been successfully used in a number of areas such as energy and production planning, telecommunications, and transportation. Recently, the practical experience gained in stochastic programming has been expanded to a much larger spectrum of applications including financial modeling, risk management, and probabilistic risk analysis. Major topics in this volume include: (1) advances in theory and implementation of stochastic programming algorithms; (2) sensitivity analysis of stochastic systems; (3) stochastic programming applications and other related topics. Audience: Researchers and academies working in optimization, computer modeling, operations research and financial engineering. The book is appropriate as supplementary reading in courses on optimization and financial engineering.

Modeling, Stochastic Control, Optimization, and Applications

Author : George Yin
Publisher : Springer
ISBN 13 : 3030254984
Total Pages : 599 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Modeling, Stochastic Control, Optimization, and Applications by : George Yin

Download or read book Modeling, Stochastic Control, Optimization, and Applications written by George Yin and published by Springer. This book was released on 2019-07-16 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.

American-Type Options

Author : Dmitrii S. Silvestrov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110389908
Total Pages : 672 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis American-Type Options by : Dmitrii S. Silvestrov

Download or read book American-Type Options written by Dmitrii S. Silvestrov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-03-03 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematical presentation of stochastic approximation methods 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 volume presents 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.

On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps

Author : Erhan Bayraktar
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (13 download)

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Book Synopsis On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps by : Erhan Bayraktar

Download or read book On the Perpetual American Put Options for Level Dependent Volatility Models with Jumps written by Erhan Bayraktar and published by . This book was released on 2014 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is C2 except at the stopping boundary and that it is C1 everywhere (i.e. the smooth pasting condition always holds).

Advanced Mathematical Methods for Finance

Author : Julia Di Nunno
Publisher : Springer Science & Business Media
ISBN 13 : 364218412X
Total Pages : 532 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Advanced Mathematical Methods for Finance by : Julia Di Nunno

Download or read book Advanced Mathematical Methods for Finance written by Julia Di Nunno and published by Springer Science & Business Media. This book was released on 2011-03-29 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents innovations in the mathematical foundations of financial analysis and numerical methods for finance and applications to the modeling of risk. The topics selected include measures of risk, credit contagion, insider trading, information in finance, stochastic control and its applications to portfolio choices and liquidation, models of liquidity, pricing, and hedging. The models presented are based on the use of Brownian motion, Lévy processes and jump diffusions. Moreover, fractional Brownian motion and ambit processes are also introduced at various levels. The chosen blend of topics gives an overview of the frontiers of mathematics for finance. New results, new methods and new models are all introduced in different forms according to the subject. Additionally, the existing literature on the topic is reviewed. The diversity of the topics makes the book suitable for graduate students, researchers and practitioners in the areas of financial modeling and quantitative finance. The chapters will also be of interest to experts in the financial market interested in new methods and products. This volume presents the results of the European ESF research networking program Advanced Mathematical Methods for Finance.

Stochastic Analysis, Stochastic Systems, and Applications to Finance

Author : Allanus Hak-Man Tsoi
Publisher : World Scientific
ISBN 13 : 9814355704
Total Pages : 274 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Stochastic Analysis, Stochastic Systems, and Applications to Finance by : Allanus Hak-Man Tsoi

Download or read book Stochastic Analysis, Stochastic Systems, and Applications to Finance written by Allanus Hak-Man Tsoi and published by World Scientific. This book was released on 2011 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces some advanced topics in probability theories ? both pure and applied ? is divided into two parts. The first part deals with the analysis of stochastic dynamical systems, in terms of Gaussian processes, white noise theory, and diffusion processes. The second part of the book discusses some up-to-date applications of optimization theories, martingale measure theories, reliability theories, stochastic filtering theories and stochastic algorithms towards mathematical finance issues such as option pricing and hedging, bond market analysis, volatility studies and asset trading modeling.

Stochastic Processes, Statistical Methods, and Engineering Mathematics

Author : Anatoliy Malyarenko
Publisher : Springer Nature
ISBN 13 : 3031178203
Total Pages : 907 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Stochastic Processes, Statistical Methods, and Engineering Mathematics by : Anatoliy Malyarenko

Download or read book Stochastic Processes, Statistical Methods, and Engineering Mathematics written by Anatoliy Malyarenko and published by Springer Nature. This book was released on 2023-01-26 with total page 907 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the 2019 conference on Stochastic Processes and Algebraic Structures held in SPAS2019, Västerås, Sweden, from September 30th to October 2nd 2019, was to showcase the frontiers of research in several important areas of mathematics, mathematical statistics, and its applications. The conference was organized around the following topics 1. Stochastic processes and modern statistical methods,2. Engineering mathematics,3. Algebraic structures and their applications. The conference brought together a select group of scientists, researchers, and practitioners from the industry who are actively contributing to the theory and applications of stochastic, and algebraic structures, methods, and models. The conference provided early stage researchers with the opportunity to learn from leaders in the field, to present their research, as well as to establish valuable research contacts in order to initiate collaborations in Sweden and abroad. New methods for pricing sophisticated financial derivatives, limit theorems for stochastic processes, advanced methods for statistical analysis of financial data, and modern computational methods in various areas of applied science can be found in this book. The principal reason for the growing interest in these questions comes from the fact that we are living in an extremely rapidly changing and challenging environment. This requires the quick introduction of new methods, coming from different areas of applied science. Advanced concepts in the book are illustrated in simple form with the help of tables and figures. Most of the papers are self-contained, and thus ideally suitable for self-study. Solutions to sophisticated problems located at the intersection of various theoretical and applied areas of the natural sciences are presented in these proceedings.

Financial Modelling with Jump Processes

Author : Peter Tankov
Publisher : CRC Press
ISBN 13 : 1135437947
Total Pages : 552 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Financial Modelling with Jump Processes by : Peter Tankov

Download or read book Financial Modelling with Jump Processes written by Peter Tankov and published by CRC Press. This book was released on 2003-12-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic

American Options Under Stochastic Volatility

Author : Arun Chockalingam
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (129 download)

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Book Synopsis American Options Under Stochastic Volatility by : Arun Chockalingam

Download or read book American Options Under Stochastic Volatility written by Arun Chockalingam and published by . This book was released on 2012 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of pricing an American option written on an underlying asset with constant price volatility has been studied extensively in literature. Real-world data, however, demonstrates that volatility is not constant and stochastic volatility models are used to account for dynamic volatility changes. Option pricing methods that have been developed in literature for pricing under stochastic volatility focus mostly on European options. We consider the problem of pricing American options under stochastic volatility which has relatively had much less attention from literature. First, we develop an exercise-policy improvement procedure to compute the optimal exercise policy and option price. We show that the scheme monotonically converges for various popular stochastic volatility models in literature. Second, using this computational tool, we explore a variety of questions that seek insights into the dependence of option prices, exercise policies and implied volatilities on the market price of volatility risk and correlation between the asset and stochastic volatility.

Dynamic Hedging

Author : Nassim Nicholas Taleb
Publisher : John Wiley & Sons
ISBN 13 : 9780471152804
Total Pages : 536 pages
Book Rating : 4.1/5 (528 download)

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Book Synopsis Dynamic Hedging by : Nassim Nicholas Taleb

Download or read book Dynamic Hedging written by Nassim Nicholas Taleb and published by John Wiley & Sons. This book was released on 1997-01-14 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Destined to become a market classic, Dynamic Hedging is the only practical reference in exotic options hedgingand arbitrage for professional traders and money managers Watch the professionals. From central banks to brokerages to multinationals, institutional investors are flocking to a new generation of exotic and complex options contracts and derivatives. But the promise of ever larger profits also creates the potential for catastrophic trading losses. Now more than ever, the key to trading derivatives lies in implementing preventive risk management techniques that plan for and avoid these appalling downturns. Unlike other books that offer risk management for corporate treasurers, Dynamic Hedging targets the real-world needs of professional traders and money managers. Written by a leading options trader and derivatives risk advisor to global banks and exchanges, this book provides a practical, real-world methodology for monitoring and managing all the risks associated with portfolio management. Nassim Nicholas Taleb is the founder of Empirica Capital LLC, a hedge fund operator, and a fellow at the Courant Institute of Mathematical Sciences of New York University. He has held a variety of senior derivative trading positions in New York and London and worked as an independent floor trader in Chicago. Dr. Taleb was inducted in February 2001 in the Derivatives Strategy Hall of Fame. He received an MBA from the Wharton School and a Ph.D. from University Paris-Dauphine.

Trading Volatility

Author : Colin Bennett
Publisher :
ISBN 13 : 9781461108757
Total Pages : 316 pages
Book Rating : 4.1/5 (87 download)

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Book Synopsis Trading Volatility by : Colin Bennett

Download or read book Trading Volatility written by Colin Bennett and published by . This book was released on 2014-08-17 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication aims to fill the void between books providing an introduction to derivatives, and advanced books whose target audience are members of quantitative modelling community. In order to appeal to the widest audience, this publication tries to assume the least amount of prior knowledge. The content quickly moves onto more advanced subjects in order to concentrate on more practical and advanced topics. "A master piece to learn in a nutshell all the essentials about volatility with a practical and lively approach. A must read!" Carole Bernard, Equity Derivatives Specialist at Bloomberg "This book could be seen as the 'volatility bible'!" Markus-Alexander Flesch, Head of Sales & Marketing at Eurex "I highly recommend this book both for those new to the equity derivatives business, and for more advanced readers. The balance between theory and practice is struck At-The-Money" Paul Stephens, Head of Institutional Marketing at CBOE "One of the best resources out there for the volatility community" Paul Britton, CEO and Founder of Capstone Investment Advisors "Colin has managed to convey often complex derivative and volatility concepts with an admirable simplicity, a welcome change from the all-too-dense tomes one usually finds on the subject" Edmund Shing PhD, former Proprietary Trader at BNP Paribas "In a crowded space, Colin has supplied a useful and concise guide" Gary Delany, Director Europe at the Options Industry Council