Switching Levy Models in Continuous Time PDF Download

Author: Kyriakos Chourdakis
Publisher:
ISBN:
Category :
Languages : en
Pages : 39

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Book Description
This paper introduces a general regime switching Levy process, and constructs the characteristic function in closed form. Correlations between the underlying Markov chain and the asset returns are also allowed, by imposing asset price jumps whenever a regime change takes place. Based on the characteristic function the conditional densities and vanilla option prices can be rapidly computed using FFT. It is shown that the regime switching model has the potential to capture a wide variety of implied volatility skews. The paper also discusses the pricing of exotic contracts, like barrier, Bermudan and American options, by implementation of a quadrature method. A detailed numerical experiment illustrates the application of the regime switching framework.

Author: Kyriakos M. Chourdakis
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Svetlozar T. Rachev
Publisher: John Wiley & Sons
ISBN: 0470937262
Category : Business & Economics
Languages : en
Pages : 316

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Book Description
An in-depth guide to understanding probability distributions and financial modeling for the purposes of investment management In Financial Models with Lévy Processes and Volatility Clustering, the expert author team provides a framework to model the behavior of stock returns in both a univariate and a multivariate setting, providing you with practical applications to option pricing and portfolio management. They also explain the reasons for working with non-normal distribution in financial modeling and the best methodologies for employing it. The book's framework includes the basics of probability distributions and explains the alpha-stable distribution and the tempered stable distribution. The authors also explore discrete time option pricing models, beginning with the classical normal model with volatility clustering to more recent models that consider both volatility clustering and heavy tails. Reviews the basics of probability distributions Analyzes a continuous time option pricing model (the so-called exponential Lévy model) Defines a discrete time model with volatility clustering and how to price options using Monte Carlo methods Studies two multivariate settings that are suitable to explain joint extreme events Financial Models with Lévy Processes and Volatility Clustering is a thorough guide to classical probability distribution methods and brand new methodologies for financial modeling.

Author: Andreas E. Kyprianou
Publisher: Springer Science & Business Media
ISBN: 3642376320
Category : Mathematics
Languages : en
Pages : 461

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Book Description
Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their application appears in the theory of many areas of classical and modern stochastic processes including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance, continuous-state branching processes and positive self-similar Markov processes. This textbook is based on a series of graduate courses concerning the theory and application of Lévy processes from the perspective of their path fluctuations. Central to the presentation is the decomposition of paths in terms of excursions from the running maximum as well as an understanding of short- and long-term behaviour. 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 tractability. The second edition additionally addresses recent developments in the potential analysis of subordinators, Wiener-Hopf theory, the theory of scale functions and their application to ruin theory, as well as including an extensive overview of the classical and modern theory of positive self-similar Markov processes. Each chapter has a comprehensive set of exercises.

Author: Charles Shaw
Publisher:
ISBN:
Category :
Languages : en
Pages : 21

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Book Description
A regime-switching Levy framework, where all parameter values depend on the value of a continuous time Markov chain as per Chevallier and Goutte (2017), is employed to study US Corporate Option-Adjusted Spreads (OASs). For modelling purposes we assume a Normal Inverse Gaussian distribution, allowing heavier tails and skewness. After the Expectation-Maximization algorithm is applied to this general class of regime switching models, we compare the obtained results with time series models without jumps, including one with regime switching and one without. We find that a regime-switching Levy model clearly defines two regimes for A-, AA-, and AAA-rated OASs. We find further evidence of regime-switching effects, with data showing relatively pronounced jump intensity around the time of major crisis periods, thereby confirming the presence and importance of volatility regimes. Results indicate that ignoring the complex and dynamic dependence structure in favour of certain model assumptions may lead to a significant underestimation of risk.

Author: Anatoliy Swishchuk
Publisher: Springer
ISBN: 331932408X
Category : Mathematics
Languages : en
Pages : 140

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Book Description
This book is devoted to the history of Change of Time Methods (CTM), the connections of CTM to stochastic volatilities and finance, fundamental aspects of the theory of CTM, basic concepts, and its properties. An emphasis is given on many applications of CTM in financial and energy markets, and the presented numerical examples are based on real data. The change of time method is applied to derive the well-known Black-Scholes formula for European call options, and to derive an explicit option pricing formula for a European call option for a mean-reverting model for commodity prices. Explicit formulas are also derived for variance and volatility swaps for financial markets with a stochastic volatility following a classical and delayed Heston model. The CTM is applied to price financial and energy derivatives for one-factor and multi-factor alpha-stable Levy-based models. Readers should have a basic knowledge of probability and statistics, and some familiarity with stochastic processes, such as Brownian motion, Levy process and martingale.

Author: Anatoliy V. Swishchuk
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
In this paper, we show how to calculate the price of zero-coupon bonds for many Gaussian and Levy one-factor and multi-factor models of r(t) using change of time method. These models include, in particular, Ornshtein-Uhlenbeck (1930), Vasicek (1977), Cox-Ingersoll-Ross (1985), continuous-time GARCH, Ho-Lee (1986), Hull-White (1990) and Heath-Jarrrow-Morton (1992) models and their various combinations. We also derive partial integro-differential equations (PIDEs) for the values of swaps, caps, floors and options on them, swaptions, captions and floortions, respectively. We apply the change of time method to price the interest rate derivatives for the interest rates r(t) described by various stochastic differential equations driven by alpha-stable Levy processes.

Author: Harry Markowitz
Publisher: World Scientific
ISBN: 981283365X
Category : Business & Economics
Languages : en
Pages : 719

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Book Description
Harry M Markowitz received the Nobel Prize in Economics in 1990 for his pioneering work in portfolio theory. He also received the von Neumann Prize from the Institute of Management Science and the Operations Research Institute of America in 1989 for his work in portfolio theory, sparse matrices and the SIMSCRIPT computer language. While Dr Markowitz is well-known for his work on portfolio theory, his work on sparse matrices remains an essential part of linear optimization calculations. In addition, he designed and developed SIMSCRIPT OCo a computer programming language. SIMSCRIPT has been widely used for simulations of systems such as air transportation and communication networks."

Author: Oliver Ibe
Publisher: Newnes
ISBN: 0124078397
Category : Mathematics
Languages : en
Pages : 515

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Book Description
Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects. Therefore, this is an applications-oriented book that also includes enough theory to provide a solid ground in the subject for the reader. Presents both the theory and applications of the different aspects of Markov processes Includes numerous solved examples as well as detailed diagrams that make it easier to understand the principle being presented Discusses different applications of hidden Markov models, such as DNA sequence analysis and speech analysis.

Author: G. George Yin
Publisher: Springer Science & Business Media
ISBN: 1441911057
Category : Mathematics
Languages : en
Pages : 398

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Book Description
This book encompasses the study of hybrid switching di usion processes and their applications. The word \hybrid" signi es the coexistence of c- tinuous dynamics and discrete events, which is one of the distinct features of the processes under consideration. Much of the book is concerned with the interactions of the continuous dynamics and the discrete events. Our motivations for studying such processes originate from emerging and - isting applications in wireless communications, signal processing, queueing networks, production planning, biological systems, ecosystems, nancial engineering, and modeling, analysis, and control and optimization of lar- scale systems, under the in uence of random environments. Displaying mixture distributions, switching di usions may be described by the associated operators or by systems of stochastic di erential eq- tions together with the probability transition laws of the switching actions. We either have Markov-modulated switching di usions or processes with continuous state-dependent switching. The latter turns out to be much more challenging to deal with. Viewing the hybrid di usions as a number of di usions joined together by the switching process, they may be se- ingly not much di erent from their di usion counterpart. Nevertheless, the underlying problems become more di cult to handle, especially when the switching processes depend on continuous states. The di culty is due to the interaction of the discrete and continuous processes and the tangled and hybrid information pattern.