Real Options Under A Double Exponential Jump Diffusion Model With Regime Switching And Partial Information
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| Author | : Pengfei Luo |
| Publisher | : |
| Total Pages | : 34 |
| Release | : 2015 |
| Genre | : |
| ISBN | : |
We consider an irreversible investment in a project, which generates cash flow following a double exponential jump-diffusion process and its expected return is governed by a continuous-time two-state Markov chain. If the expected return is observable, we present explicit expressions for the pricing and timing of the option to invest. With partial information, i.e. if the expected return is unobservable, we provide an explicit project value and an integral-differential equation for the pricing and timing of the option. We show a method to measure the information value, i.e. the difference between the values of the option to invest under the two cases. We present numerical solutions by finite difference methods if jumps are absent. By numerical analysis, we find that: (i) The value of the option to invest increases with the belief on economic boom; (ii) If investors are more uncertain about the state of the economy, information is more valuable; (iii) The more likely the transition from boom to recession, the less the value of the option; (iv) The bigger the dispersion of the expected return, the higher the information value; (v) A higher cash flow volatility induces a less information value.
| Author | : S?ren Asmussen |
| Publisher | : World Scientific |
| Total Pages | : 621 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 9814282529 |
The book gives a comprehensive treatment of the classical and modern ruin probability theory. Some of the topics are Lundberg's inequality, the Cramr?Lundberg approximation, exact solutions, other approximations (e.g., for heavy-tailed claim size distributions), finite horizon ruin probabilities, extensions of the classical compound Poisson model to allow for reserve-dependent premiums, Markov-modulation, periodicity, change of measure techniques, phase-type distributions as a computational vehicle and the connection to other applied probability areas, like queueing theory. In this substantially updated and extended second version, new topics include stochastic control, fluctuation theory for Levy processes, Gerber?Shiu functions and dependence.
| Author | : Bernt Øksendal |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 263 |
| Release | : 2007-04-26 |
| Genre | : Mathematics |
| ISBN | : 3540698264 |
Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.
| Author | : Stefano M. Iacus |
| Publisher | : John Wiley & Sons |
| Total 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.
| Author | : Rogemar S. Mamon |
| Publisher | : Springer |
| Total Pages | : 280 |
| Release | : 2014-05-14 |
| Genre | : Business & Economics |
| ISBN | : 1489974423 |
Since the groundbreaking research of Harry Markowitz into the application of operations research to the optimization of investment portfolios, finance has been one of the most important areas of application of operations research. The use of hidden Markov models (HMMs) has become one of the hottest areas of research for such applications to finance. This handbook offers systemic applications of different methodologies that have been used for decision making solutions to the financial problems of global markets. As the follow-up to the authors’ Hidden Markov Models in Finance (2007), this offers the latest research developments and applications of HMMs to finance and other related fields. Amongst the fields of quantitative finance and actuarial science that will be covered are: interest rate theory, fixed-income instruments, currency market, annuity and insurance policies with option-embedded features, investment strategies, commodity markets, energy, high-frequency trading, credit risk, numerical algorithms, financial econometrics and operational risk. Hidden Markov Models in Finance: Further Developments and Applications, Volume II presents recent applications and case studies in finance and showcases the formulation of emerging potential applications of new research over the book’s 11 chapters. This will benefit not only researchers in financial modeling, but also others in fields such as engineering, the physical sciences and social sciences. Ultimately the handbook should prove to be a valuable resource to dynamic researchers interested in taking full advantage of the power and versatility of HMMs in accurately and efficiently capturing many of the processes in the financial market.
| Author | : Fabrice D. Rouah |
| Publisher | : John Wiley & Sons |
| Total Pages | : 437 |
| Release | : 2013-08-01 |
| Genre | : Business & Economics |
| ISBN | : 1118695178 |
Tap into the power of the most popular stochastic volatility model for pricing equity derivatives Since its introduction in 1993, the Heston model has become a popular model for pricing equity derivatives, and the most popular stochastic volatility model in financial engineering. This vital resource provides a thorough derivation of the original model, and includes the most important extensions and refinements that have allowed the model to produce option prices that are more accurate and volatility surfaces that better reflect market conditions. The book's material is drawn from research papers and many of the models covered and the computer codes are unavailable from other sources. The book is light on theory and instead highlights the implementation of the models. All of the models found here have been coded in Matlab and C#. This reliable resource offers an understanding of how the original model was derived from Ricatti equations, and shows how to implement implied and local volatility, Fourier methods applied to the model, numerical integration schemes, parameter estimation, simulation schemes, American options, the Heston model with time-dependent parameters, finite difference methods for the Heston PDE, the Greeks, and the double Heston model. A groundbreaking book dedicated to the exploration of the Heston model—a popular model for pricing equity derivatives Includes a companion website, which explores the Heston model and its extensions all coded in Matlab and C# Written by Fabrice Douglas Rouah a quantitative analyst who specializes in financial modeling for derivatives for pricing and risk management Engaging and informative, this is the first book to deal exclusively with the Heston Model and includes code in Matlab and C# for pricing under the model, as well as code for parameter estimation, simulation, finite difference methods, American options, and more.
| Author | : Dean Paxson |
| Publisher | : Elsevier |
| Total Pages | : 345 |
| Release | : 2002-12-05 |
| Genre | : Business & Economics |
| ISBN | : 0080497977 |
Real R&D options are among the earliest modelled real options, with now ten primary practical uses: general R&D planning, planning R&D in stages, evaluating test information, new product development timing, operations, abandonment, risk sharing, market funding, industry strategy and regulation. This book was partly motivated by requests to identify and develop real option models for R&D in telecommunications, petroleum technology and biotechnology. Nine new models cover information and implementation costs, analytical solutions for mean reverting, or fat tailed revenues, endogenous learning and exogenous and experiential shocks, American sequential options, and innovator advantages. Four new applications include forward start development options, exploration options, innovation with information costs, and innovator's real values with changing market share. R&D directors and researchers will find several uses for these models: - general R&D planning - evaluating test information - new product development timing - risk sharing - industry strategy and regulation - A practical guide to how organizations can use Real Option techniques to effectively value research and development by companies - Provides a rigorous theoretical underpinning of the use of Real Option techniques - Real Options applications are orientated around the economies of North America, Europe and Asia, for an international perspective
| Author | : Allanus Hak-Man Tsoi |
| Publisher | : World Scientific |
| Total Pages | : 274 |
| Release | : 2011 |
| Genre | : Business & Economics |
| ISBN | : 9814355712 |
Pt. I. Stochastic analysis and systems. 1. Multidimensional Wick-Ito formula for Gaussian processes / D. Nualart and S. Ortiz-Latorre. 2. Fractional white noise multiplication / A.H. Tsoi. 3. Invariance principle of regime-switching diffusions / C. Zhu and G. Yin -- pt. II. Finance and stochastics. 4. Real options and competition / A. Bensoussan, J.D. Diltz and S.R. Hoe. 5. Finding expectations of monotone functions of binary random variables by simulation, with applications to reliability, finance, and round robin tournaments / M. Brown, E.A. Pekoz and S.M. Ross. 6. Filtering with counting process observations and other factors : applications to bond price tick data / X. Hu, D.R. Kuipers and Y. Zeng. 7. Jump bond markets some steps towards general models in applications to hedging and utility problems / M. Kohlmann and D. Xiong. 8. Recombining tree for regime-switching model : algorithm and weak convergence / R.H. Liu. 9. Optimal reinsurance under a jump diffusion model / S. Luo. 10. Applications of counting processes and martingales in survival analysis / J. Sun. 11. Stochastic algorithms and numerics for mean-reverting asset trading / Q. Zhang, C. Zhuang and G. Yin
| Author | : Samuel N Cohen |
| Publisher | : World Scientific |
| Total Pages | : 605 |
| Release | : 2012-08-10 |
| Genre | : Mathematics |
| ISBN | : 9814483915 |
This book consists of a series of new, peer-reviewed papers in stochastic processes, analysis, filtering and control, with particular emphasis on mathematical finance, actuarial science and engineering. Paper contributors include colleagues, collaborators and former students of Robert Elliott, many of whom are world-leading experts and have made fundamental and significant contributions to these areas.This book provides new important insights and results by eminent researchers in the considered areas, which will be of interest to researchers and practitioners. The topics considered will be diverse in applications, and will provide contemporary approaches to the problems considered. The areas considered are rapidly evolving. This volume will contribute to their development, and present the current state-of-the-art stochastic processes, analysis, filtering and control.Contributing authors include: H Albrecher, T Bielecki, F Dufour, M Jeanblanc, I Karatzas, H-H Kuo, A Melnikov, E Platen, G Yin, Q Zhang, C Chiarella, W Fleming, D Madan, R Mamon, J Yan, V Krishnamurthy.
| Author | : Robert J Elliott |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 374 |
| Release | : 2008-09-27 |
| Genre | : Science |
| ISBN | : 0387848541 |
As more applications are found, interest in Hidden Markov Models continues to grow. Following comments and feedback from colleagues, students and other working with Hidden Markov Models the corrected 3rd printing of this volume contains clarifications, improvements and some new material, including results on smoothing for linear Gaussian dynamics. In Chapter 2 the derivation of the basic filters related to the Markov chain are each presented explicitly, rather than as special cases of one general filter. Furthermore, equations for smoothed estimates are given. The dynamics for the Kalman filter are derived as special cases of the authors’ general results and new expressions for a Kalman smoother are given. The Chapters on the control of Hidden Markov Chains are expanded and clarified. The revised Chapter 4 includes state estimation for discrete time Markov processes and Chapter 12 has a new section on robust control.
