Author: Kyriakos M. ChourdakisPublisher:
ISBN:
Category : Economics
Languages : en
Pages : 45
Book Description
Stochastic Volatility and Jumps Driven by Continuous Time Markov Chains
Author: Kyriakos M. ChourdakisPublisher:
ISBN:
Category : Economics
Languages : en
Pages : 45
Book Description
Stochastic Volatility and Jumps Driven by Continuous Time Markov Chains
Author: Kyriakos ChourdakisPublisher:
ISBN:
Category :
Languages : en
Pages : 47
Book Description
This paper considers a model where there is a single state variable that drives the state of the world and therefore the asset price behavior. This variable evolves according to a multi-state continuous time Markov chain, as the continuous time counterpart of (Hamilton 1989) model. It derives the moment generating function of the asset log-price difference under very general assumptions about its stochastic process, incorporating volatility and jumps that can follow virtually any distribution, both of them being driven by the same state variable. For an illustration, the extreme value distribution is used as the jump distribution. The paper shows how GMM and conditional ML estimators can be constructed, generalizing Hamilton's filter for the continuous time case. The risk neutral process is constructed and contingent claim prices under this specification are derived, in the lines of (Bakshi and Madan 2000). Finally, an empirical example is set up, to illustrate the potential benefits of the model.
Stochastic Volatility and Jumps Driven by Continous Time Markov Chains
Author: Kyriakos M. ChourdakisPublisher:
ISBN:
Category :
Languages : en
Pages : 45
Book Description
Continuous-Time Markov Chains
Author: William J. AndersonPublisher: Springer Science & Business Media
ISBN: 1461230381
Category : Mathematics
Languages : en
Pages : 367
Book Description
Continuous time parameter Markov chains have been useful for modeling various random phenomena occurring in queueing theory, genetics, demography, epidemiology, and competing populations. This is the first book about those aspects of the theory of continuous time Markov chains which are useful in applications to such areas. It studies continuous time Markov chains through the transition function and corresponding q-matrix, rather than sample paths. An extensive discussion of birth and death processes, including the Stieltjes moment problem, and the Karlin-McGregor method of solution of the birth and death processes and multidimensional population processes is included, and there is an extensive bibliography. Virtually all of this material is appearing in book form for the first time.
Markov Chains
Author: Pierre BremaudPublisher: Springer Science & Business Media
ISBN: 1475731248
Category : Mathematics
Languages : en
Pages : 456
Book Description
Primarily an introduction to the theory of stochastic processes at the undergraduate or beginning graduate level, the primary objective of this book is to initiate students in the art of stochastic modelling. However it is motivated by significant applications and progressively brings the student to the borders of contemporary research. Examples are from a wide range of domains, including operations research and electrical engineering. Researchers and students in these areas as well as in physics, biology and the social sciences will find this book of interest.
The Journal of Derivatives
Author: Multivariate Continuous Time Stochastic Volatility Models Driven by a Lévy Process
Author: Robert Josef StelzerPublisher:
ISBN:
Category :
Languages : en
Pages : 249
Book Description
Markov Processes for Stochastic Modeling
Author: Masaaki KijimaPublisher: Springer
ISBN: 1489931325
Category : Mathematics
Languages : en
Pages : 345
Book Description
This book presents an algebraic development of the theory of countable state space Markov chains with discrete- and continuous-time parameters. A Markov chain is a stochastic process characterized by the Markov prop erty that the distribution of future depends only on the current state, not on the whole history. Despite its simple form of dependency, the Markov property has enabled us to develop a rich system of concepts and theorems and to derive many results that are useful in applications. In fact, the areas that can be modeled, with varying degrees of success, by Markov chains are vast and are still expanding. The aim of this book is a discussion of the time-dependent behavior, called the transient behavior, of Markov chains. From the practical point of view, when modeling a stochastic system by a Markov chain, there are many instances in which time-limiting results such as stationary distributions have no meaning. Or, even when the stationary distribution is of some importance, it is often dangerous to use the stationary result alone without knowing the transient behavior of the Markov chain. Not many books have paid much attention to this topic, despite its obvious importance.
Markov Chains
Author: David FreedmanPublisher: Springer Science & Business Media
ISBN: 1461255007
Category : Mathematics
Languages : en
Pages : 395
Book Description
A long time ago I started writing a book about Markov chains, Brownian motion, and diffusion. I soon had two hundred pages of manuscript and my publisher was enthusiastic. Some years and several drafts later, I had a thousand pages of manuscript, and my publisher was less enthusiastic. So we made it a trilogy: Markov Chains Brownian Motion and Diffusion Approximating Countable Markov Chains familiarly - MC, B & D, and ACM. I wrote the first two books for beginning graduate students with some knowledge of probability; if you can follow Sections 10.4 to 10.9 of Markov Chains you're in. The first two books are quite independent of one another, and completely independent of the third. This last book is a monograph which explains one way to think about chains with instantaneous states. The results in it are supposed to be new, except where there are specific disclaim ers; it's written in the framework of Markov Chains. Most of the proofs in the trilogy are new, and I tried hard to make them explicit. The old ones were often elegant, but I seldom saw what made them go. With my own, I can sometimes show you why things work. And, as I will VB1 PREFACE argue in a minute, my demonstrations are easier technically. If I wrote them down well enough, you may come to agree.
Smile Pricing Explained
Author: P. AustingPublisher: Springer
ISBN: 1137335726
Category : Business & Economics
Languages : en
Pages : 235
Book Description
Smile Pricing Explained provides a clear and thorough explanation of the concepts of smile modelling that are at the forefront of modern derivatives pricing. The key models used in practice are covered, together with numerical techniques and calibration.