Download or read book The Valuation of American Options on Multiple Assets written by Jerome Detemple and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we provide valuation formulas for several types of American options on two or more assets. First we characterize the optimal exercise regions and provide valuation formulas for a number of American option contracts on multiple underlying assets with convex payoff functions. Examples include options on the maximum of two assets, dual strike options, spread options, exchange options, options on the product and powers of the product, and options on the arithmetic average of two assets. Second, we also consider a class of contracts with non-convex payoffs, such as American capped exchange options. For this option we explicitly identify the optimal exercise boundary and provide a decomposition of the price in terms of a capped exchange option with automatic exercise at the cap and an early exercise premium involving the benefits of exercising prior to reaching the cap.
Download or read book The Valuation of American Options on Multiple Assets written by Detemple, Jérôme and published by Montréal : CIRANO. This book was released on 1994 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Valuation of American Options on Single Asset and Multiple Assets written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
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.
Download or read book Exercise Regions of American Options on Several Assets written by Stephane Villeneuve 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 study the nonemptiness and the shape of the exercise region of American options written on several assets. Our contribution is threefold. First, we state an analytic theorem which characterizes the nonemptiness of the exercise region. Second, we study a particular class of payoff functions for which we explicitly identify the shape and the asymptotic behavior near maturity of the associated exercise region. Finally, we present additional results which complement the Broadie and Detemple results concerning the valuation of various types of American options on several assets.
Download or read book American Type Options written by Dmitrii S. Silvestrov and published by Walter de Gruyter. This book was released on 2013-11-27 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Accelerating American Option Pricing in Lattices written by Michael Curran and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This article describes a method of accelerating the pricing of American options in binomial lattices in a Black-Scholes environment. The standard backward induction method for solving an option valuation problem involves computations at every node of the binomial option price tree. We show that many of the intermediate calculations are actually unnecessary, and eliminating them leads to a dramatic increase in computational efficiency. Test cases demonstrate that valuing an American put option can be accelerated by at least an order of magnitude, while yielding the identical estimate given by the standard Cox, Ross, and Rubinstein binomial tree. In addition, we discuss how similar techniques may be applied to pricing American options on interest rate derivatives and options involving multiple assets.
Download or read book Numerical Methods in Finance written by L. C. G. Rogers and published by Cambridge University Press. This book was released on 1997-06-26 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods in Finance describes a wide variety of numerical methods used in financial analysis.
Download or read book Accelerating American Option Pricing in Lattices written by Mike Curran and published by . This book was released on 2015 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article describes a method of accelerating the pricing of American options in binomial lattices in a Black-Scholes environment. The standard backward induction method for solving an option valuation problem involves computations at every node of the binomial option price tree. We show that many of the intermediate calculations are actually unnecessary, and eliminating them leads to a dramatic increase in computational efficiency.Test cases demonstrate that valuing an American put option can be accelerated by at least an order of magnitude, while yielding the identical estimate given by the standard Cox, Ross, and Rubenstein binomial tree. In addition, we discuss how similar techniques may be applied to pricing American options on interest rate derivatives and options involving multiple assets.
Download or read book Game Theory and Applications Volume 11 written by Leon Petrosjan and published by Nova Publishers. This book was released on 2007 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together papers of well-known specialists in game theory and adjacent problems. It presents the basic results in dynamic games, stochastic games, applications of game theoretical methods in ecology and economics and methodological aspects of game theory.
Download or read book On the Valuation of American Exchange Options written by Andreas Andrikopoulos and published by . This book was released on 2009 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt: We adopt a quadratic approach to the valuation of the option to exchange one asset for another, when the option owner has the right to exercise prior to option expiration. Accurate pricing results are obtained and tested against competitive models in the literature, building on the hypothesis that option value is the product of two functions, one being a function of time, and the other one being a function of the stock prices.
Download or read book Option Pricing Interest Rates and Risk Management written by Elyès Jouini and published by Cambridge University Press. This book was released on 2001 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2001 handbook surveys the state of practice, method and understanding in the field of mathematical finance. Every chapter has been written by leading researchers and each starts by briefly surveying the existing results for a given topic, then discusses more recent results and, finally, points out open problems with an indication of what needs to be done in order to solve them. The primary audiences for the book are doctoral students, researchers and practitioners who already have some basic knowledge of mathematical finance. In sum, this is a comprehensive reference work for mathematical finance and will be indispensable to readers who need to find a quick introduction or reference to a specific topic, leading all the way to cutting edge material.
Download or read book The Valuation of American Options on Bonds written by T. S. Ho and published by . This book was released on 1997 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The valuation of American-style bond options involves two important aspects that need to be modeled carefully. First, stochastic interest rates influence the volatility of the price of the bond, the underlying asset, in a complex fashion as the bond approaches maturity, and hence, the incremental value of the early exercise (American) feature. Second, the early exercise decision for such options is affected by the term structure of interest rates on future dates, since the live value of the claim on each future date depends on the discount rates on that date. These two aspects are modeling in this paper. The paper analyzes the value of American options on bonds using a generalization of the Geske-Johnson (1984) technique. The method uses as inputs the valuation of European options, and options with multiple exercise dates. It is proved that a risk-neutral valuation relationship along the lines of the Black-Scholes (1973) model holds for options exercisable on multiple dates, even under stochastic interest rates, when the price of the underlying asset is lognormally distributed. The proposed computational method uses the maximized value of these options, where the maximization is over all possible exercise dates. The value of the American option is then computed by Richardson extrapolation. The volatility of the underlying default-free bond is modeled using a two-factor model, with a short-term and a long-term interest rate factor. The paper reports the results of simulations of American option values and show how they vary with the key parameter inputs, such as the maturity of the bond, its volatility, and the option strike price.
Download or read book Numerical Solution of Stochastic Differential Equations with Jumps in Finance written by Eckhard Platen and published by Springer Science & Business Media. This book was released on 2010-07-23 with total page 868 pages. Available in PDF, EPUB and Kindle. Book excerpt: In financial and actuarial modeling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations (1992). The present monograph builds on the above-mentioned work and provides an introduction to stochastic differential equations with jumps, in both theory and application, emphasizing the numerical methods needed to solve such equations. It presents many new results on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector, extrapolation, Markov chain and variance reduction methods, stressing the importance of their numerical stability. Furthermore, it includes chapters on exact simulation, estimation and filtering. Besides serving as a basic text on quantitative methods, it offers ready access to a large number of potential research problems in an area that is widely applicable and rapidly expanding. Finance is chosen as the area of application because much of the recent research on stochastic numerical methods has been driven by challenges in quantitative finance. Moreover, the volume introduces readers to the modern benchmark approach that provides a general framework for modeling in finance and insurance beyond the standard risk-neutral approach. It requires undergraduate background in mathematical or quantitative methods, is accessible to a broad readership, including those who are only seeking numerical recipes, and includes exercises that help the reader develop a deeper understanding of the underlying mathematics.
Download or read book Martingale Methods in Financial Modelling written by Marek Musiela and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and self-contained treatment of the theory and practice of option pricing. The role of martingale methods in financial modeling is exposed. The emphasis is on using arbitrage-free models already accepted by the market as well as on building the new ones. Standard calls and puts together with numerous examples of exotic options such as barriers and quantos, for example on stocks, indices, currencies and interest rates are analysed. The importance of choosing a convenient numeraire in price calculations is explained. Mathematical and financial language is used so as to bring mathematicians closer to practical problems of finance and presenting to the industry useful maths tools.
Download or read book Dynamic Asset Pricing Theory written by Darrell Duffie and published by Princeton University Press. This book was released on 2010-01-27 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a thoroughly updated edition of Dynamic Asset Pricing Theory, the standard text for doctoral students and researchers on the theory of asset pricing and portfolio selection in multiperiod settings under uncertainty. The asset pricing results are based on the three increasingly restrictive assumptions: absence of arbitrage, single-agent optimality, and equilibrium. These results are unified with two key concepts, state prices and martingales. Technicalities are given relatively little emphasis, so as to draw connections between these concepts and to make plain the similarities between discrete and continuous-time models. Readers will be particularly intrigued by this latest edition's most significant new feature: a chapter on corporate securities that offers alternative approaches to the valuation of corporate debt. Also, while much of the continuous-time portion of the theory is based on Brownian motion, this third edition introduces jumps--for example, those associated with Poisson arrivals--in order to accommodate surprise events such as bond defaults. Applications include term-structure models, derivative valuation, and hedging methods. Numerical methods covered include Monte Carlo simulation and finite-difference solutions for partial differential equations. Each chapter provides extensive problem exercises and notes to the literature. A system of appendixes reviews the necessary mathematical concepts. And references have been updated throughout. With this new edition, Dynamic Asset Pricing Theory remains at the head of the field.
