Option Pricing with Continuous-time Markov Chain Regime Switching
Title | Option Pricing with Continuous-time Markov Chain Regime Switching PDF eBook |
Author | Craig Steven Edwards |
Publisher | |
Pages | 198 |
Release | 2004 |
Genre | |
ISBN |
Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing
Title | Continuous-Time Markov Chain and Regime Switching Approximations with Applications to Options Pricing PDF eBook |
Author | Zhenyu Cui |
Publisher | |
Pages | 32 |
Release | 2019 |
Genre | |
ISBN |
In this chapter, we present recent developments in using the tools of continuous-time Markov chains for the valuation of European and path-dependent financial derivatives. We also survey results on a newly proposed regime switching approximation to stochastic volatility, and stochastic local volatility models. The presented framework is part of an exciting recent stream of literature on numerical option pricing, and offers a new perspective that combines the theory of diffusion processes, Markov chains, and Fourier techniques. It is also elegantly connected to partial differential equation (PDE) approaches.
Switching Levy Models in Continuous Time
Title | Switching Levy Models in Continuous Time PDF eBook |
Author | Kyriakos Chourdakis |
Publisher | |
Pages | 39 |
Release | 2008 |
Genre | |
ISBN |
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.
Modeling, Stochastic Control, Optimization, and Applications
Title | Modeling, Stochastic Control, Optimization, and Applications PDF eBook |
Author | George Yin |
Publisher | Springer |
Pages | 599 |
Release | 2019-07-16 |
Genre | Mathematics |
ISBN | 3030254984 |
This volume collects papers, based on invited talks given at the IMA workshop in Modeling, Stochastic Control, Optimization, and Related Applications, held at the Institute for Mathematics and Its Applications, University of Minnesota, during May and June, 2018. There were four week-long workshops during the conference. They are (1) stochastic control, computation methods, and applications, (2) queueing theory and networked systems, (3) ecological and biological applications, and (4) finance and economics applications. For broader impacts, researchers from different fields covering both theoretically oriented and application intensive areas were invited to participate in the conference. It brought together researchers from multi-disciplinary communities in applied mathematics, applied probability, engineering, biology, ecology, and networked science, to review, and substantially update most recent progress. As an archive, this volume presents some of the highlights of the workshops, and collect papers covering a broad range of topics.
Continuous-Time Markov Chains and Applications
Title | Continuous-Time Markov Chains and Applications PDF eBook |
Author | G. George Yin |
Publisher | Springer Science & Business Media |
Pages | 442 |
Release | 2012-11-14 |
Genre | Mathematics |
ISBN | 1461443466 |
This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted to applications in controlled dynamic systems, production planning, and numerical methods for controlled Markovian systems with large-scale and complex structures in the real-world problems. This second edition has been updated throughout and includes two new chapters on asymptotic expansions of solutions for backward equations and hybrid LQG problems. The chapters on analytic and probabilistic properties of two-time-scale Markov chains have been almost completely rewritten and the notation has been streamlined and simplified. This book is written for applied mathematicians, engineers, operations researchers, and applied scientists. Selected material from the book can also be used for a one semester advanced graduate-level course in applied probability and stochastic processes.
Application of Continuous Time Markov Chain Models
Title | Application of Continuous Time Markov Chain Models PDF eBook |
Author | Chia Chun Lo |
Publisher | |
Pages | 454 |
Release | 2009 |
Genre | |
ISBN |
Option Pricing and Estimation of Financial Models with R
Title | Option Pricing and Estimation of Financial Models with R PDF eBook |
Author | Stefano M. Iacus |
Publisher | John Wiley & Sons |
Pages | 402 |
Release | 2011-02-23 |
Genre | Business & Economics |
ISBN | 1119990203 |
Presents inference and simulation of stochastic process in the field of model calibration for financial times series modelled by continuous time processes and numerical option pricing. Introduces the bases of probability theory and goes on to explain how to model financial times series with continuous models, how to calibrate them from discrete data and further covers option pricing with one or more underlying assets based on these models. Analysis and implementation of models goes beyond the standard Black and Scholes framework and includes Markov switching models, Lévy models and other models with jumps (e.g. the telegraph process); Topics other than option pricing include: volatility and covariation estimation, change point analysis, asymptotic expansion and classification of financial time series from a statistical viewpoint. The book features problems with solutions and examples. All the examples and R code are available as an additional R package, therefore all the examples can be reproduced.