Download or read book Closed Form Analytic Pricing and Hedging of Arithmetic Asian Options Using a Reciprocal Gamma Distribution written by Moshe A. Milevsky and published by . This book was released on 2008 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we develop a better approximation for the price and hedging parameters of an arithmetic Asian option. We demonstrate that the distribution of the sum of a sequence of asset prices can be better approximated by the Reciprocal Gamma (as opposed to Lognormal) density function. In fact, in the limit, the distribution of the sum converges precisely to the Reciprocal Gamma density. Consequently, we are able to obtain a closed-form analytic expression for the price and hedging parameters of an Asian option which is theoretically justified, as well as more accurate, than the widely used lognormal approximation. We compare our results with previously published tables and formulas (that have appeared in RISK) and conclude that, not only is our formula easy-to-use and explain, our method is at least as good as any other algorithm available in the literature.
Download or read book Asian Options the Sum of Lognormals and the Reciprocal Gamma Distribution written by Moshe A. Milevsky and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Arithmetic Asian options are difficult to price and hedge as they do not have closed-form analytic solutions. The main theoretical reason for this difficulty is that the payoff depends on the finite sum of correlated lognormal variables, which is not lognormal and for which there is no recognizable probability density function. We use elementary techniques to derive the probability density function of the infinite sum of correlated lognormal random variables and show that it is reciprocal gamma distributed, under suitable parameter restrictions. A random variable is reciprocal gamma distributed if its inverse is gamma distributed. We use this result to approximate the finite sum of correlated lognormal variables and then value arithmetic Asian options using the reciprocal gamma distribution as the state-price density function. We thus obtain a closed-form analytic expression for the value of an arithmetic Asian option, where the cumulative density function of the gamma distribution, G(d) in our formula, plays the exact same role as N(d) in the Black-Scholes/Merton formula. In addition to being theoretically justified and exact in the limit, we compare our method against other algorithms in the literature and show our method is quicker, at least as accurate, and, in our opinion, more intuitive and pedagogically appealing than any previously published result, especially when applied to high yielding currency options.
Download or read book Quantitative Analysis In Financial Markets Collected Papers Of The New York University Mathematical Finance Seminar written by Marco Avellaneda and published by World Scientific. This book was released on 1999-10-27 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book contains lectures delivered at the celebrated Seminar in Mathematical Finance at the Courant Institute. The lecturers and presenters of papers are prominent researchers and practitioners in the field of quantitative financial modeling. Most are faculty members at leading universities or Wall Street practitioners.The lectures deal with the emerging science of pricing and hedging derivative securities and, more generally, managing financial risk. Specific articles concern topics such as option theory, dynamic hedging, interest-rate modeling, portfolio theory, price forecasting using statistical methods, etc.
Download or read book Arithmetic Asian Options with Continuous Sampling written by Jin E. Zhang and published by . This book was released on 1999 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Complete Analytical Solution of the Asian Option Pricing and Asian Option Value at Risk Problems written by Alexander Izmailov and published by . This book was released on 2015 with total page 13 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 publication “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” (see link 'http://ssrn.com/abstract=2489601' http://ssrn.com/abstract=2489601).•In this paper we report similar unique results for Asian Options, enabling complete analytical resolution of all problems associated with Asian Options. •Our discovery of the Asian Option probability density function enables exact closed-form analytical results for its expected value (price) for the first time without depending on Inverse Laplace or Fourier transforms that only abbreviate complex numerical integration procedures. •Expected value is the first moment. 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, such as Inverse Laplace or Fourier transforms, now used to represent the first moment. •Our formulation of the Asian Option probability density function is general enough to cover interesting and practical cases that are not addressed in the literature at all: for example, cases for which the averaging period is a terminal subset of the contract period, e.g. the last 3 months of the option lifetime. •Our formulation of the Asian Option probability density function 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 an Asian Option will be below or above any set of thresholds at any future time before or at termination. Such assessments are absolutely out of reach of current published methods for treating Asian Options.•Resolution of the Asian Option Pricing problem enables knowledge of their linear correlation with Vanilla Options and, therefore, hedging in terms of Vanilla Options. Moreover, an opportunity to construct “synthetic” Asian Options from Vanilla Options for a given termination becomes a trivial exercise. •All numerical evaluations based on our analytical results are practically instantaneous and absolutely accurate.
Download or read book Handbook of Quantitative Finance and Risk Management written by Cheng-Few Lee and published by Springer Science & Business Media. This book was released on 2010-06-14 with total page 1700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantitative finance is a combination of economics, accounting, statistics, econometrics, mathematics, stochastic process, and computer science and technology. Increasingly, the tools of financial analysis are being applied to assess, monitor, and mitigate risk, especially in the context of globalization, market volatility, and economic crisis. This two-volume handbook, comprised of over 100 chapters, is the most comprehensive resource in the field to date, integrating the most current theory, methodology, policy, and practical applications. Showcasing contributions from an international array of experts, the Handbook of Quantitative Finance and Risk Management is unparalleled in the breadth and depth of its coverage. Volume 1 presents an overview of quantitative finance and risk management research, covering the essential theories, policies, and empirical methodologies used in the field. Chapters provide in-depth discussion of portfolio theory and investment analysis. Volume 2 covers options and option pricing theory and risk management. Volume 3 presents a wide variety of models and analytical tools. Throughout, the handbook offers illustrative case examples, worked equations, and extensive references; additional features include chapter abstracts, keywords, and author and subject indices. From "arbitrage" to "yield spreads," the Handbook of Quantitative Finance and Risk Management will serve as an essential resource for academics, educators, students, policymakers, and practitioners.
Download or read book A Complete Analytical Solution of the Asian Option Pricing Within the Heston Model for Stochastic Volatility written by Alexander Izmailov and published by . This book was released on 2015 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first ever explicit formulation of the concept of the 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” and “Complete Analytical Solution of the Asian Option Pricing and Asian Option Value-at-Risk Problems. A Probability Density Function Approach.” See links: 'http://ssrn.com/abstract=2489601' http://ssrn.com/abstract=2489601 and 'http://ssrn.com/abstract=2546430' http://ssrn.com/abstract=2546430.The first ever explicit formulation of the concept of the options' probability density functions within the framework of stochastic volatility (Heston model) has been introduced in our publications “Complete Analytical Solution of the Heston Model for Option Pricing and Value-at-Risk Problems: A Probability Density Function Approach”, “Complete Analytical Solution of the American Style Option Pricing with Constant and Stochastic Volatilities: A Probability Density Function Approach” and “A Complete Analytical Resolution of the Double Barrier Option's Pricing Within the Heston Model. A Probability Density Approach.” See links:'http://ssrn.com /abstract=2549033' http://ssrn.com/abstract=2549033 and 'http://ssrn.com/abstract=2554038' http://ssrn.com/abstract=2554038 and 'http://ssrn.com/abstract=2605948' http://ssrn.com/abstract=2605948.In this paper we report complete analytical closed-form results for the European style Asian Options considered within the Heston model for Stochastic Volatility (SV). Our discovery of the probability density function of the European style Asian Options with SV enables exact closed-form representation of its expected value (price) for the first time ever. Our formulation of the probability density function for the European style Asian Options with SV is expressive enough to enable derivation for the first time ever of corollary analytical closed-form results for such Value-At-Risk characteristics as the probabilities that an Asian Option with SV will be below or above any threshold at any future time before or at termination. Such assessments are absolutely out of reach of the current published methods for treating Asian Options even in the framework of constant volatility.All numerical evaluations based on our analytical results are practically instantaneous and absolutely accurate.
Download or read book Pricing of American Style Fixed Strike Asian Options with Continuous Arithmetic Average written by Seung-Young Oh and published by . This book was released on 2004 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article explores the analytic valuation of American-style fixed strike Asian option or average rate option based on the continuous arithmetic average in the Black-Scholes framework. Because there is no closed-form exact valuation formula for the average rate option with the arithmetic average, a very well-approximated arithmetic average density function is used for the valuation. The optimal exercise boundary and the values of American average rate options are compared with those of American plain vanilla options. Especially, this article shows that American average rate option can have two different optimal exercise boundaries depending on the parameters. Numerical experiments are also performed to demonstrate the influence of the component factors on the values of American average rate options and to illustrate the accuracy and efficiency of the valuation formula.
Download or read book Financial Econometrics Mathematics and Statistics written by Cheng-Few Lee and published by Springer. This book was released on 2019-06-03 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: This rigorous textbook introduces graduate students to the principles of econometrics and statistics with a focus on methods and applications in financial research. Financial Econometrics, Mathematics, and Statistics introduces tools and methods important for both finance and accounting that assist with asset pricing, corporate finance, options and futures, and conducting financial accounting research. Divided into four parts, the text begins with topics related to regression and financial econometrics. Subsequent sections describe time-series analyses; the role of binomial, multi-nomial, and log normal distributions in option pricing models; and the application of statistics analyses to risk management. The real-world applications and problems offer students a unique insight into such topics as heteroskedasticity, regression, simultaneous equation models, panel data analysis, time series analysis, and generalized method of moments. Written by leading academics in the quantitative finance field, allows readers to implement the principles behind financial econometrics and statistics through real-world applications and problem sets. This textbook will appeal to a less-served market of upper-undergraduate and graduate students in finance, economics, and statistics.
Download or read book Theory of Continously sampled Asian Option Pricing written by Jin E. Zhang and published by . This book was released on 2000 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Efficient and Stable Method for Short Maturity Asian Options written by Rupak Chatterjee and published by . This book was released on 2017 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we develop a Markov chain-based approximation method to price arithmetic Asian options for short maturities under the case of geometric Brownian motion. It has the advantage of being a closed-form approximation involving only matrices. It is an accurate, efficient, and stable method for the pricing and hedging of short maturity arithmetic Asian options for which previous methods in the literature have shown either slower convergence or instabilities in hedging parameters. We also consider the pricing and hedging of floating-strike Asian options and fixed-strike in-progress Asian options, and demonstrate that our method is as good as and sometimes better than existing approximation methods in the literature.
Download or read book A New Fast and Robust Technique for Pricing and Hedging Asia Options written by Georgios Vasileiou Dalakouras and published by . This book was released on 2004 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Multinational Finance Journal written by and published by . This book was released on 2003 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Commodity Asian Options written by Gianluca Fusai and published by . This book was released on 2008 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: We compute an analytical expression for the moment generating function of the joint random vector consisting of a spot price and its discretely monitored average for a large class of square-root price dynamics. This result, combined with the Fourier transform pricing method proposed by Carr and Madan (1999) [Carr, P., Madan D., 1999. Option valuation using the fast Fourier transform. Journal of Computational Finance 2(4), Summer, 61-73] allows us to derive a closed-form formula for the fair value of discretely-monitored Asian-style options. Our analysis encompasses the case of commodity price dynamics displaying mean reversion and jointly fitting a quoted futures curve and the seasonal structure of spot price volatility. Four tests are conducted to assess the relative performance of the pricing procedure stemming from our formulae. Empirical results based on natural gas data from NYMEX and corn data from CBOT show a remarkable improvement over the main alternative techniques developed for pricing Asian-style options within the market standard framework of geometric Brownian motion.
Download or read book PIDE and Solution Related to Pricing of L evy Driven Arithmetic Type Floating Asian Options written by Sudip Chandra and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a stochastic model to develop a pricing partial integro-differential equation (PIDE) and its Fourier transform expression for floating Asian options based on the It ^o-L 'evy calculus. The stock price is driven by a class of infinite activity L 'evy processes leading to the market inherently incomplete, and dynamic hedging is no longer risk free. We first develop a PIDE for floating Asian options, and apply the Fourier transform to derive a pricing expression. Our main contribution is to develop a PIDE with its closed form pricing expression for the contract. The procedure is easy to implement for all class of L 'evy processes. Finally, the model is calibrated with the market data and its accuracy is presented.
Download or read book Quantitative Analysis in Financial Markets written by Marco Avellaneda and published by World Scientific. This book was released on 1999 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains lectures presented at the Courant Institute's Mathematical Finance Seminar.
Download or read book Monte Carlo Simulation and Finance written by Don L. McLeish and published by John Wiley & Sons. This book was released on 2011-09-13 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods have been used for decades in physics, engineering, statistics, and other fields. Monte Carlo Simulation and Finance explains the nuts and bolts of this essential technique used to value derivatives and other securities. Author and educator Don McLeish examines this fundamental process, and discusses important issues, including specialized problems in finance that Monte Carlo and Quasi-Monte Carlo methods can help solve and the different ways Monte Carlo methods can be improved upon. This state-of-the-art book on Monte Carlo simulation methods is ideal for finance professionals and students. Order your copy today.
