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Option Pricing And Hedging For Regime Switching Geometric Brownian Motion Models
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Book Synopsis Option Pricing and Hedging for Regime-Switching Geometric Brownian Motion Models by : Bruno Remillard
Download or read book Option Pricing and Hedging for Regime-Switching Geometric Brownian Motion Models written by Bruno Remillard and published by . This book was released on 2016 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We find the variance-optimal equivalent martingale measure when multivariate assets are modeled by a regime-switching geometric Brownian motion, and the regimes are represented by a homogeneous continuous time Markov chain. Under this new measure, the Markov chain driving the regimes is no longer homogeneous, which differs from the equivalent martingale measures usually proposed in the literature. We show the solution minimizes the mean-variance hedging error under the objective measure. As argued by Schweizer (1996), the variance-optimal equivalent measure naturally extends canonical option pricing results to the case of an incomplete market and the expectation under the proposed measure may be interpreted as an option price. Solutions for the option value and the optimal hedging strategy are easily obtained from Monte Carlo simulations. Two applications are considered.
Book Synopsis Options Pricing and Hedging in a Regime-Switching Volatility Model by : Melissa Anne Mielkie
Download or read book Options Pricing and Hedging in a Regime-Switching Volatility Model written by Melissa Anne Mielkie and published by . This book was released on 2014 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Both deterministic and stochastic volatility models have been used to price and hedge options. Observation of real market data suggests that volatility, while stochastic, is well modelled as alternating between two states. Under this two-state regime-switching framework, we derive coupled pricing partial differential equations (PDEs) with the inclusion of a state-dependent market price of volatility risk (MPVR) term. Since there is no closed-form solution for this pricing problem, we apply and compare two approaches to solving the coupled PDEs, assuming constant Poisson intensities. First we solve the problem using numerical solution techniques, through the application of the Crank- Nicolson numerical scheme. We also obtain approximate solutions in terms of known Black- Scholes formulae by reformulating our problem and applying the Cauchy-Kowalevski PDE theorem. Both our pricing equations and our approximate solutions give way to the analysis of the impact of our state-dependent MPVR on theoretical option prices. Using financially intuitive constraints on our option prices and Deltas, we prove the necessity of a negative MPVR. An exploration of the regime-switching option prices and their implied volatilities is given, as well as numerical results and intuition supporting our mathematical proofs. Given our regime-switching framework, there are several different hedging strategies to investigate. We consider using an option to hedge against a potential regime shift. Some practical problems arise with this approach, which lead us to set up portfolios containing a basket of two hedging options. To be more precise, we consider the effects of an option going too far in- and out-of-the-money on our hedging strategy, and introduce limits on the magnitude of such hedging option positions. A complementary approach, where constant volatility is assumed and investor's risk preferences are taken into account, is also analysed. Analysis of empirical data supports the hypothesis that volatility levels are a effected by upcoming financial events. Finally, we present an extension of our regime-switching framework with deterministic Poisson intensities. In particular, we investigate the impact of time and stock varying Poisson intensities on option prices and their corresponding implied volatilities, using numerical solution techniques. A discussion of some event-driven hedging strategies is given.
Book Synopsis Option Pricing with Regime Switching by : Bong-Gyu Jang
Download or read book Option Pricing with Regime Switching written by Bong-Gyu Jang and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper presents a new method for evaluating European options with regime switching. We represent their value as a sum of integrations over simplexes and show the integrations can be approximated by the method of Grundmann and Moller (1978). The method is applicable to the valuation of European-type options written on the underlying asset whose price follows a regime-switching mean-reverting process as well as a classical regime-switching geometric Brownian motion. Numerical examples give us evidences that it can be a powerful tool for practitioners in option pricing.
Book Synopsis Option Pricing and Hedging for Discrete Time Regime-Switching Models by : Bruno Remillard
Download or read book Option Pricing and Hedging for Discrete Time Regime-Switching Models written by Bruno Remillard and published by . This book was released on 2014 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose optimal mean-variance dynamic hedging strategies in discrete time under a multivariate Gaussian regime-switching model. The methodology, which also performs pricing, is robust to time-varying and clustering risk observed in financial time series. As such, it overcomes the main theoretical drawbacks of the Black-Scholes model. To support our approach, we provide univariate pricing results for monthly S&P 500 vanilla options. Then, we present the associated out-of-sample hedging results in the context of harvesting the implied versus realized volatility premium. Using the proposed methodology, the Sharpe ratio derived from the strategy doubles over the classical Black-Scholes delta-hedging methodology.
Book Synopsis Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems by : Houmin Yan
Download or read book Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems written by Houmin Yan and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume contains 16 research articles. It presents recent and pressing issues in stochastic processes, control theory, differential games, optimization, and their applications in finance, manufacturing, queueing networks, and climate control. One of the salient features is that the book is highly multi-disciplinary. The book is dedicated to Professor Suresh Sethi on the occasion of his 60th birthday, in view of his distinguished career.
Book Synopsis Innovations In Insurance, Risk- And Asset Management - Proceedings Of The Innovations In Insurance, Risk- And Asset Management Conference by : Kathrin Glau
Download or read book Innovations In Insurance, Risk- And Asset Management - Proceedings Of The Innovations In Insurance, Risk- And Asset Management Conference written by Kathrin Glau and published by World Scientific. This book was released on 2018-09-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent developments in the interdisciplinary fields of actuarial science, quantitative finance, risk- and asset management. The authors are leading experts from academia and practice who participated in Innovations in Insurance, Risk- and Asset Management, an international conference held at the Technical University of Munich in 2017.The topics covered include the mathematics of extreme risks, systemic risk, model uncertainty, interest rate and hybrid models, alternative investments, dynamic investment strategies, quantitative risk management, asset liability management, liability driven investments, and behavioral finance.This timely selection of topics is highly relevant for the financial industry and addresses current issues both from an academic as well as from a practitioner's point of view.
Book Synopsis Volatility Surface and Term Structure by : Kin Keung Lai
Download or read book Volatility Surface and Term Structure written by Kin Keung Lai and published by Routledge. This book was released on 2013-09-11 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides different financial models based on options to predict underlying asset price and design the risk hedging strategies. Authors of the book have made theoretical innovation to these models to enable the models to be applicable to real market. The book also introduces risk management and hedging strategies based on different criterions. These strategies provide practical guide for real option trading. This book studies the classical stochastic volatility and deterministic volatility models. For the former, the classical Heston model is integrated with volatility term structure. The correlation of Heston model is considered to be variable. For the latter, the local volatility model is improved from experience of financial practice. The improved local volatility surface is then used for price forecasting. VaR and CVaR are employed as standard criterions for risk management. The options trading strategies are also designed combining different types of options and they have been proven to be profitable in real market. This book is a combination of theory and practice. Users will find the applications of these financial models in real market to be effective and efficient.
Book Synopsis Energy and Power Risk Management by : Alexander Eydeland
Download or read book Energy and Power Risk Management written by Alexander Eydeland and published by John Wiley & Sons. This book was released on 2003-02-03 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for Energy and Power Risk Management "Energy and Power Risk Management identifies and addresses the key issues in the development of the turbulent energy industry and the challenges it poses to market players. An insightful and far-reaching book written by two renowned professionals." -Helyette Geman, Professor of Finance University Paris Dauphine and ESSEC "The most up-to-date and comprehensive book on managing energy price risk in the natural gas and power markets. An absolute imperative for energy traders and energy risk management professionals." -Vincent Kaminski, Managing Director Citadel Investment Group LLC "Eydeland and Wolyniec's work does an excellent job of outlining the methods needed to measure and manage risk in the volatile energy market." -Gerald G. Fleming, Vice President, Head of East Power Trading, TXU Energy Trading "This book combines academic rigor with real-world practicality. It is a must-read for anyone in energy risk management or asset valuation." -Ron Erd, Senior Vice President American Electric Power
Book Synopsis Option Hedging and Valuation Under Stochastic Volatility by : Joshua Rosenberg
Download or read book Option Hedging and Valuation Under Stochastic Volatility written by Joshua Rosenberg and published by . This book was released on 1996 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities by : Anatoli? Vital?evich Svishchuk
Download or read book Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities written by Anatoli? Vital?evich Svishchuk and published by World Scientific. This book was released on 2013 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities is devoted to the modeling and pricing of various kinds of swaps, such as those for variance, volatility, covariance, correlation, for financial and energy markets with different stochastic volatilities, which include CIR process, regime-switching, delayed, mean-reverting, multi-factor, fractional, Levy-based, semi-Markov and COGARCH(1,1). One of the main methods used in this book is change of time method. The book outlines how the change of time method works for different kinds of models and problems arising in financial and energy markets and the associated problems in modeling and pricing of a variety of swaps. The book also contains a study of a new model, the delayed Heston model, which improves the volatility surface fitting as compared with the classical Heston model. The author calculates variance and volatility swaps for this model and provides hedging techniques. The book considers content on the pricing of variance and volatility swaps and option pricing formula for mean-reverting models in energy markets. Some topics such as forward and futures in energy markets priced by multi-factor Levy models and generalization of Black-76 formula with Markov-modulated volatility are part of the book as well, and it includes many numerical examples such as S&P60 Canada Index, S&P500 Index and AECO Natural Gas Index.
Book Synopsis Mathematical Modeling and Methods of Option Pricing by : Lishang Jiang
Download or read book Mathematical Modeling and Methods of Option Pricing written by Lishang Jiang and published by World Scientific. This book was released on 2005 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the perspective of partial differential equations (PDE), this book introduces the Black-Scholes-Merton's option pricing theory. A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs.
Book Synopsis Basis Options Delta Hedging by : Robert Brooks
Download or read book Basis Options Delta Hedging written by Robert Brooks and published by . This book was released on 2005 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: The difference between a basis option pricing model on futures or forward contracts, assuming both underlying futures contracts follow geometric Brownian motion, and a basis option pricing model on futures contracts, assuming both underlying securities follow arithmetic Brownian motion are non material from a risk management perspective. We show this by demonstrating that the differences in the deltas and gammas of the two models are not materially different. This being the case, the normal assumption on the underlying futures contracts can be made easing the risk management computational burden.
Book Synopsis Telegraph Processes and Option Pricing by : Nikita Ratanov
Download or read book Telegraph Processes and Option Pricing written by Nikita Ratanov and published by Springer Nature. This book was released on 2023-01-04 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stochastic Analysis, Stochastic Systems, and Applications to Finance by : Allanus Hak-Man Tsoi
Download or read book Stochastic Analysis, Stochastic Systems, and Applications to Finance written by Allanus Hak-Man Tsoi and published by World Scientific. This book was released on 2011 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces some advanced topics in probability theories ? both pure and applied ? is divided into two parts. The first part deals with the analysis of stochastic dynamical systems, in terms of Gaussian processes, white noise theory, and diffusion processes. The second part of the book discusses some up-to-date applications of optimization theories, martingale measure theories, reliability theories, stochastic filtering theories and stochastic algorithms towards mathematical finance issues such as option pricing and hedging, bond market analysis, volatility studies and asset trading modeling.
Book Synopsis Hidden Markov Models in Finance by : Rogemar S. Mamon
Download or read book Hidden Markov Models in Finance written by Rogemar S. Mamon and published by Springer Science & Business Media. This book was released on 2007-04-26 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of methodologies have been employed to provide decision making solutions globalized markets. Hidden Markov Models in Finance offers the first systematic application of these methods to specialized financial problems: option pricing, credit risk modeling, volatility estimation and more. The book provides tools for sorting through turbulence, volatility, emotion, chaotic events – the random "noise" of financial markets – to analyze core components.
Book Synopsis Option Pricing and Estimation of Financial Models with R by : Stefano M. Iacus
Download or read book Option Pricing and Estimation of Financial Models with R written by Stefano M. Iacus and published by John Wiley & Sons. This book was released on 2011-02-23 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Option Pricing Under Regime Switching (analytical, PDE, and FFT Methods) by : Mohammad Yousef Akhavein Sohrabi
Download or read book Option Pricing Under Regime Switching (analytical, PDE, and FFT Methods) written by Mohammad Yousef Akhavein Sohrabi and published by . This book was released on 2011 with total page 83 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although globally used in option pricing, the Black-Scholes model has not been able to reflect the evolution of stocks in the real world. A regime-switching model which allows jumps in the underlying asset prices and the parameters of the corresponding stochastic process is more accurate. We evaluate the analytical solution for pricing of European options under a two-state regime switching model. Both the convergence of the analytical solution and the feature of implied volatility are investigated through numerical examples.
