Author: Brice V. Dupoyet Publisher: ISBN: Category : Languages : en Pages : 16
Book Description
This article proposes and tests a convenient, easy to use closed-form solution for the pricing of a European Call option where the underlying asset is subject to upward and downward jumps displaying separate distributions and probabilities of occurrence. The setup presented in this article lays in contrast to the assumption of lognormality in the jump magnitude generally made in the option pricing literature and can be used by academics and practitioners alike as it allows for a more precise modeling of the implied volatility smile. Through the use of both simulations and actual options data on the Samp;P 500 index it is shown that the asymmetric jump model captures deviations from the standard geometric Brownian motion with more precision than the lognormal jump setup is able to achieve.
Author: Wojbor A. Woyczyński Publisher: CRC Press ISBN: 1000475352 Category : Mathematics Languages : en Pages : 138
Book Description
Diffusion Processes, Jump Processes, and Stochastic Differential Equations provides a compact exposition of the results explaining interrelations between diffusion stochastic processes, stochastic differential equations and the fractional infinitesimal operators. The draft of this book has been extensively classroom tested by the author at Case Western Reserve University in a course that enrolled seniors and graduate students majoring in mathematics, statistics, engineering, physics, chemistry, economics and mathematical finance. The last topic proved to be particularly popular among students looking for careers on Wall Street and in research organizations devoted to financial problems. Features Quickly and concisely builds from basic probability theory to advanced topics Suitable as a primary text for an advanced course in diffusion processes and stochastic differential equations Useful as supplementary reading across a range of topics.
Author: Cyrus A. Ramezani Publisher: ISBN: Category : Languages : en Pages : 32
Book Description
An asymmetric jump-diffusion model of stock price behavior is proposed. In an extension of Merton's (1976), we posit that returns dynamics are determined by a drift component, a Wiener process and two jump processes representing the arrival of quot;goodquot; or quot;badquot; news that lead to jumps in security prices. We assume that good and bad news may arrive with different intensities and the distribution of jump magnitudes representing each type is different. To admit and test these distinctions, we assume that news arrives according to two Poisson processes and jump magnitudes representing good and bad news are Pareto and Beta distributed. We develop cumulant and maximum likelihood estimators and use daily stock prices data to estimate the proposed model. Empirical results strongly support the posited model. Likelihood based test provides support to the hypothesis that stock prices respond differently to the arrival of good and bad news.
Author: Samuel Frame Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
The hypothesis that asset returns are log-normally distributed has been widely rejected. The extant literature has shown that empirical asset returns are highly skewed and leptokurtic (fat tails). The Affine Jump-Diffusion (AJD) model improves upon the log-normal specification by adding a jump component to the return process. The two-sided jump-diffusion (TSJD) model further improves upon the AJD specification by allowing for the tail behavior of the return distribution to be asymmetrical. The Pareto-Beta (Ramezani and Zeng, 1998) and the Double Exponential (Kou, 2002) models present two alternative TSJD specifications. Under the Pareto-Beta specification, two Poisson processes govern the arrival rate of good and bad news, leading to Pareto distributed up-jumps or Beta distributed down-jumps in prices. Under the Double Exponential specification, a single Poisson process generates jumps in returns but the up and down magnitudes are generated by two exponential distributions. Both specifications results in highly asymmetric jump diffusion processes with desirable empirical and theoretical features. Accordingly, these models have been widely adopted in the portfolio choice, option pricing, and other branches of the literature. The primary objective of this paper is to contribute to the econometric methods for estimating the parameters of the TSJD models. Relying on the Bayesian approach, we develop a Markov Chain Monte Carlo (MCMC) estimation technique that is appropriate to these specifications. We then provide an empirical assessment of these model using daily returns for the S&P-500 and the NASDAQ indexes, as well as individual stocks. We complete our analysis by providing a comparison of the estimated parameters under the MCMC and the MLE methodologies.
Author: Andreas E. Kyprianou Publisher: Springer Science & Business Media ISBN: 3540313435 Category : Mathematics Languages : en Pages : 382
Book Description
This textbook forms the basis of a graduate course on the theory and applications of Lévy processes, from the perspective of their path fluctuations. The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction, for which recent theoretical advances have yielded a higher degree of mathematical transparency and explicitness.
Author: Nikita Ratanov Publisher: Springer Nature ISBN: 3662658275 Category : Mathematics Languages : en Pages : 451
Book Description
This book provides an extensive, systematic overview of the modern theory of telegraph processes and their multidimensional counterparts, together with numerous fruitful applications in financial modelling. Focusing on stochastic processes of bounded variation instead of classical diffusion, or more generally, Lévy processes, has two obvious benefits. First, the mathematical technique is much simpler, which helps to concentrate on the key problems of stochastic analysis and applications, including financial market modelling. Second, this approach overcomes some shortcomings of the (parabolic) nature of classical diffusions that contradict physical intuition, such as infinite propagation velocity and infinite total variation of paths. In this second edition, some sections of the previous text are included without any changes, while most others have been expanded and significantly revised. These are supplemented by predominantly new results concerning piecewise linear processes with arbitrary sequences of velocities, jump amplitudes, and switching intensities. The chapter on functionals of the telegraph process has been significantly expanded by adding sections on exponential functionals, telegraph meanders and running extrema, the times of the first passages of telegraph processes with alternating random jumps, and distribution of the Euclidean distance between two independent telegraph processes. A new chapter on the multidimensional counterparts of the telegraph processes is also included. The book is intended for graduate students in mathematics, probability, statistics and quantitative finance, and for researchers working at academic institutions, in industry and engineering. It can also be used by university lecturers and professionals in various applied areas.
Author: Andrew Pole Publisher: John Wiley & Sons ISBN: 1118160738 Category : Business & Economics Languages : en Pages : 230
Book Description
While statistical arbitrage has faced some tough times?as markets experienced dramatic changes in dynamics beginning in 2000?new developments in algorithmic trading have allowed it to rise from the ashes of that fire. Based on the results of author Andrew Pole?s own research and experience running a statistical arbitrage hedge fund for eight years?in partnership with a group whose own history stretches back to the dawn of what was first called pairs trading?this unique guide provides detailed insights into the nuances of a proven investment strategy. Filled with in-depth insights and expert advice, Statistical Arbitrage contains comprehensive analysis that will appeal to both investors looking for an overview of this discipline, as well as quants looking for critical insights into modeling, risk management, and implementation of the strategy.
Author: Peter Tankov Publisher: CRC Press ISBN: 1135437947 Category : Business & Economics Languages : en Pages : 552
Book Description
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
Author: Elena Celledoni Publisher: Springer ISBN: 3030015939 Category : Mathematics Languages : en Pages : 734
Book Description
The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.
Author: Brice V. Dupoyet
Author: Wojbor A. Woyczyński
Author: Cyrus A. Ramezani
Author: Efrem Bonfiglioli
Author: Samuel Frame
Author: Andreas E. Kyprianou
Author: Nikita Ratanov
Author: Andrew Pole
Author: Peter Tankov
Author: Elena Celledoni