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Author : Fei Guan
Publisher :
ISBN 13 :
Total Pages : 32 pages
Book Rating : 4.:/5 (428 download)
Download or read book American Options Pricing on Assets with Stochastic Variances written by Fei Guan and published by . This book was released on 1998 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Arun Chockalingam
Publisher :
ISBN 13 :
Total Pages : 30 pages
Book Rating : 4.:/5 (129 download)
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.
Author : Robert F. Engle
Publisher :
ISBN 13 :
Total Pages : 48 pages
Book Rating : 4.0/5 ( download)
Download or read book Index-option Pricing with Stochastic Volatility and the Value of Accurate Variance Forecasts written by Robert F. Engle and published by . This book was released on 1993 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: In pricing primary-market options and in making secondary markets, financial intermediaries depend on the quality of forecasts of the variance of the underlying assets. Hence, the gain from improved pricing of options would be a measure of the value of a forecast of underlying asset returns. NYSE index returns over the period of 1968-1991 are used to suggest that pricing index options of up to 90-days maturity would be more accurate when: (1) using ARCH specifications in place of a moving average of squared returns; (2) using Hull and White's (1987) adjustment for stochastic variance in Black and Scholes's (1973) formula; (3) accounting explicitly for weekends and the slowdown of variance whenever the market is closed.
Author : Mark Broadie
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)
Download or read book American Options with Stochastic Dividends and Volatility written by Mark Broadie and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we consider American option contracts when the underlying asset has stochastic dividends and stochastic volatility. We provide a full discussion of the theoretical foundations of American option valuation and exercise boundaries. We show how they depend on the various sources of uncertainty which drive dividend rates and volatility, and derive equilibrium asset prices, derivative prices and optimal exercise boundaries in a general equilibrium model. The theoretical models yield fairly complex expressions which are difficult to estimate. We therefore adopt a nonparametric approach which enables us to investigate reduced forms. Indeed, we use nonparametric methods to estimate call prices and exercise boundaries conditional on dividends and volatility. Since the latter is a latent process, we propose several approaches, notably using EGARCH filtered estimates, implied and historical volatilities. The nonparametric approach allows us to test whether call prices and exercise decisions are primarily driven by dividends, as has been advocated by Harvey and Whaley (1992a,b) and Fleming and Whaley (1994) for the OEX contract, or whether stochastic volatility complements dividend uncertainty. We find that dividends alone do not account for all aspects of call option pricing and exercise decisions, suggesting a need to include stochastic volatility.
Author : Andrew M.K. Wu
Publisher :
ISBN 13 :
Total Pages : 45 pages
Book Rating : 4.:/5 (129 download)
Download or read book Arbitrage-Free Evaluation of American-Style Options on Assets with Stochastics Variance Characteristics written by Andrew M.K. Wu and published by . This book was released on 2001 with total page 45 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents an arbitrage-free framework for contingent claim valuation under stochastic volatility that does not hinge on the market price of volatility risk. It is contrary to the traditional literature, in which some restrictive equilibrium assumptions about investors' preferences must be imposed if one allows arbitrary correlation between the asset price and volatility increments. Our approach to stochastic volatility modelling relies on specifying the forward variance as a function of the market option prices under the no-arbitrage condition. The model is implemented by the Ho-Stapleton-Subrahmanyam (1995) multivariate binomial approximation procedure, but with an extension to permit the multiplicative factor to be a function of stochastic volatility within a recombining context. In conjunction with the lattice-based algorithm, the generalised Geske-Johnson (1984) technique is employed to accelerate the computational efficiency when valuing American options. The key to the model is that it exactly matches the volatility structure inferred from a portfolio of actively traded options, yet is simple enough to be used for pricing a wide class of derivative securities within a reasonable time frame. We investigate how stochastic volatility influences the early exercise premium of an American option. The magnitude of this effect depends upon the moneyness of the option, the time to maturity, the volatilities of the state variables, as well as the correlation between them.
Author : Robert F. Engle
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.:/5 (129 download)
Download or read book Index-Option Pricing with Stochastic Volatility and the Value of Accurate Variance Forecasts written by Robert F. Engle and published by . This book was released on 2010 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: In pricing primary-market options and in making secondary markets, financial intermediaries depend on the quality of forecasts of the variance of the underlying assets. Hence, the gain from improved pricing of options would be a measure of the value of a forecast of underlying asset returns. NYSE index returns over the period of 1968-1991 are used to suggest that pricing index options of up to 90-days maturity would be more accurate when: (1) using ARCH specifications in place of a moving average of squared returns; (2) using Hull and White's (1987) adjustment for stochastic variance in Black and Scholes's (1973) formula; (3) accounting explicitly for weekends and the slowdown of variance whenever the market is closed.
Author : Jonathan Ziveyi
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book American Option Pricing Under Two Stochastic Volatility Processes written by Jonathan Ziveyi and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes as proposed in Christoffersen, Heston and Jacobs (2009). We consider the associated partial differential equation (PDE) for the option price and its solution. An integral expression for the general solution of the PDE is presented by using Duhamel's principle and this is expressed in terms of the joint transition density function for the driving stochastic processes. For the particular form of the underlying dynamics we are able to solve the Kolmogorov PDE for the joint transition density function by first transforming it to a corresponding system of characteristic PDEs using a combination of Fourier and Laplace transforms. The characteristic PDE system is solved by using the method of characteristics. With the full price representation in place, numerical results are presented by first approximating the early exercise surface with a bivariate log linear function. We perform numerical comparisons with results generated by the method of lines algorithm and note that our approach provides quite good accuracy.
Author : 藍景奕
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (126 download)
Download or read book Static Hedge of American Option with Stochastic Volatility Conditional on the Asset Price written by 藍景奕 and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robert A. Jarrow
Publisher : McGraw-Hill/Irwin
ISBN 13 :
Total Pages : 268 pages
Book Rating : 4.F/5 ( download)
Download or read book Option Pricing written by Robert A. Jarrow and published by McGraw-Hill/Irwin. This book was released on 1983 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas J. Finucane
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (129 download)
Download or read book Binomial Approximations of American Call Option Prices with Stochastic Volatilities written by Thomas J. Finucane and published by . This book was released on 1998 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This study describes and tests a simple, efficient method of approximating stochastic volatility call option prices that is lattice based, and can easily accommodate the value of early exercise for American options. The proposed model exploits the fact that stochastic volatility call option prices are approximately linear in the degree of correlation between the asset price and the volatility. By calculating binomial prices for perfect and zero correlations, a simple linear function of the binomial prices can be used to accurately estimate call option prices for any other degree of correlation. A distinct advantage of the model is that it can be easily modified to price American puts.
Author : Kaushik I. Amin
Publisher :
ISBN 13 :
Total Pages : 78 pages
Book Rating : 4.:/5 (753 download)
Download or read book Pricing American Options on Risky Assets in a Stochastic Interest Rate Economy written by Kaushik I. Amin and published by . This book was released on 1991 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Andreas Kyprianou
Publisher : John Wiley & Sons
ISBN 13 : 0470017201
Total Pages : 344 pages
Book Rating : 4.4/5 (7 download)
Download or read book Exotic Option Pricing and Advanced Lévy Models written by Andreas Kyprianou and published by John Wiley & Sons. This book was released on 2006-06-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Lévy process. Working with Lévy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Lévy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Lévy markets, written by leading scientists in this field. In recent years, Lévy processes have leapt to the fore as a tractable mechanism for modeling asset returns. Exotic option values are especially sensitive to an accurate portrayal of these dynamics. This comprehensive volume provides a valuable service for financial researchers everywhere by assembling key contributions from the world's leading researchers in the field. Peter Carr, Head of Quantitative Finance, Bloomberg LP. This book provides a front-row seat to the hottest new field in modern finance: options pricing in turbulent markets. The old models have failed, as many a professional investor can sadly attest. So many of the brightest minds in mathematical finance across the globe are now in search of new, more accurate models. Here, in one volume, is a comprehensive selection of this cutting-edge research. Richard L. Hudson, former Managing Editor of The Wall Street Journal Europe, and co-author with Benoit B. Mandelbrot of The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward
Author : Stylianos Perrakis
Publisher : Springer
ISBN 13 : 3030115909
Total Pages : 277 pages
Book Rating : 4.0/5 (31 download)
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.
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 : Stephen Figlewski
Publisher : McGraw-Hill Companies
ISBN 13 : 9781556238727
Total Pages : 596 pages
Book Rating : 4.2/5 (387 download)
Download or read book Financial Options written by Stephen Figlewski and published by McGraw-Hill Companies. This book was released on 1990 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial Options links option theory with practical applications. Readers will find this book's approach simple to follow, with information organized for easy access that includes: institutional and theoretical frameworks for understanding options and option markets; how to apply option pricing models to specific types of markets; the numerical methods that must be applied to solve many option valuation problems.
Author : Boda Kang
Publisher :
ISBN 13 :
Total Pages : 49 pages
Book Rating : 4.:/5 (13 download)
Download or read book The Impact of Jumps on American Option Pricing written by Boda Kang and published by . This book was released on 2019 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper analyzes the importance of asset and volatility jumps in American option pricing models. Using the Heston (1993) stochastic volatility model with asset and volatility jumps and the Hull and White (1987) short rate model, American options are numerically evaluated by the Method of Lines. The calibration of these models to S&P 100 American options data reveals that jumps, especially asset jumps, play an important role in improving the models' ability to fit market data. Further, asset and volatility jumps tend to lift the free boundary, an effect that augments during volatile market conditions, while the additional volatility jumps marginally drift down the free boundary. As markets turn more volatile and exhibit jumps, American option holders become more prudent with their exercise decisions, especially as maturity of the options approaches.
Author : An Jiang
Publisher :
ISBN 13 :
Total Pages : 149 pages
Book Rating : 4.:/5 (975 download)
Download or read book American Spread Option Pricing with Stochastic Interest Rates written by An Jiang and published by . This book was released on 2016 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: In financial markets, spread option is a derivative security with two underlying assets and the payoff of the spread option depends on the difference of these assets. We consider American style spread option which allows the owners to exercise it at any time before the maturity. The complexity of pricing American spread option is that the boundary of the corresponding partial differential equation which determines the option price is unknown and the model for the underlying assets is two-dimensional.
