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A Direct Solution Method For Pricing Options In Regime Switching Models
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Book Synopsis A Direct Solution Method for Pricing Options in Regime-Switching Models by : Masahiko Egami
Download or read book A Direct Solution Method for Pricing Options in Regime-Switching Models written by Masahiko Egami and published by . This book was released on 2018 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pricing financial or real options with arbitrary payoffs in regime-switching models is an important problem in finance. Mathematically, it is to solve, under certain standard assumptions, a general form of optimal stopping problems in regime-switching models. In this article, we reduce an optimal stopping problem with an arbitrary value function in a two-regime environment to a pair of optimal stopping problems without regime switching. We then propose a method for finding optimal stopping rules using the techniques available for non-switching problems. In contrast to other methods, our systematic solution procedure is more direct since we first obtain the explicit form of the value functions. In the end, we discuss an option pricing problem which may not be dealt with by the conventional methods, demonstrating the simplicity of our approach.
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.
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 Pricing American Options in Regime-Switching Models by : Svetlana Boyarchenko
Download or read book Pricing American Options in Regime-Switching Models written by Svetlana Boyarchenko and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The pricing problem for American options in Markov-modulated Lévy models is solved. The early exercise boundaries and prices are calculated using a generalization of Carr's randomization procedure for regime-switching models. The pricing procedure is efficient even if the number of states is large provided the transition rates are not large w.r.t. the riskless rates. The payoffs and riskless rates may depend on a state. Special cases are stochastic volatility models and models with stochastic interest rate; both must be modeled as finite-state Markov chains. In contrast with the earlier version of the method, an explicit algorithm is formulated for wide classes of Lévy processes, and FFT and iFFT are used.
Book Synopsis Options Pricing and Risk Measures Under Regime-Switching Models by : Fangcheng Hao
Download or read book Options Pricing and Risk Measures Under Regime-Switching Models written by Fangcheng Hao and published by . This book was released on 2017-01-26 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Inference and Pricing for Regime Switching Models in Finance and Insurance by : Fangyuan Lin
Download or read book Statistical Inference and Pricing for Regime Switching Models in Finance and Insurance written by Fangyuan Lin and published by . This book was released on 2016 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis studies the estimation, goodness-of-fit testing, pricing and sampling problems for regime switching models, which are popularly used in financial markets. Specifically, we consider such models whose distributions are characterized by their characteristic functions, for example, Levy processes. The thesis contains the following contents: Chapter 1 introduces regime switching models and Levy processes. Then we present the problems we would like to address in the following chapters and our main contributions to these problems. Chapter 2 studies the estimation problem for regime switching Levy processes. We extend an existing estimation method that is based on characteristic functions to our models. Meanwhile, we compare the estimation results obtained by the proposed estimation method with those obtained by the expectation-maximization (EM) algorithm. We also address several computational challenges within the proposed estimation method. Chapter 3 studies the goodness-of-fit testing problem for regime switching models, where we extend two existing goodness-of-fit tests. Both of the proposed tests are based on characteristic functions. Chapter 4 applies the estimation and testing methods proposed in Chapters 2 and 3 to a set of S&P 500 real data. Chapter 5 studies the pricing problem for regime switching Levy processes. We propose a numerical pricing method that provides a unified pricing framework. The proposed method is illustrated by pricing European and Bermudan options and ratchet equity-index annuities (EIAs) with surrender risk. Chapter 6 studies the problem of sampling conditioned processes of regime switching models, where we propose an algorithm to sample paths from conditioned processes for a two-regime switching Black-Scholes model. Then we apply the proposed algorithm to the problems of pricing and static hedging of path-dependent options, where we use an Asian call option for illustrations. Chapter 7 lists several topics for future research.
Book Synopsis Exit Problems in Regime-Switching Models by : Svetlana Boyarchenko
Download or read book Exit Problems in Regime-Switching Models written by Svetlana Boyarchenko and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper provides a general framework for pricing of perpetual American and real options in regime-switching Levy models. In each state of the Markov chain, which determines switches from one Levy process to another one, the payoff stream is a monotone function of the Levy process labelled by the state, which allows for additional switching within each state of the Markov chain (payoffs can be different in different regions of the real line). As applications, we solve exit problems for a price-taking firm.
Book Synopsis Pricing American Options Under Regime Switching Using Method of Lines by : Carl Chiarella
Download or read book Pricing American Options Under Regime Switching Using Method of Lines written by Carl Chiarella and published by . This book was released on 2016 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers the American option pricing problem under regime-switching by using the method-of-lines (MOL) scheme. American option prices in each regime involve prices in all other regimes. We treat the prices from other regimes implicitly, thus guaranteeing consistency. Iterative procedures are required but very few iterative steps are needed in practice. Numerical tests demonstrate the robustness, accuracy and efficiency of the proposed numerical scheme. We compare our results with Buffington and Elliott (2002)'s analytical approximation under two regimes. Our MOL scheme provides improved results especially for out-of-the money options, possibly because they use a separation of variable approach to the PDEs which cannot hold around the early exercise region. We also compare our results with those of Khaliq and Liu (2009) and suggest that their implicit scheme can be improved.
Book Synopsis Exotic Option Pricing and Advanced Lévy Models by : Andreas Kyprianou
Download or read book Exotic Option Pricing and Advanced Lévy Models written by Andreas Kyprianou and published by John Wiley & Sons. This book was released on 2006-06-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since around the turn of the millennium there has been a general acceptance that one of the more practical improvements one may make in the light of the shortfalls of the classical Black-Scholes model is to replace the underlying source of randomness, a Brownian motion, by a Lévy process. Working with Lévy processes allows one to capture desirable distributional characteristics in the stock returns. In addition, recent work on Lévy processes has led to the understanding of many probabilistic and analytical properties, which make the processes attractive as mathematical tools. At the same time, exotic derivatives are gaining increasing importance as financial instruments and are traded nowadays in large quantities in OTC markets. The current volume is a compendium of chapters, each of which consists of discursive review and recent research on the topic of exotic option pricing and advanced Lévy markets, written by leading scientists in this field. In recent years, Lévy processes have leapt to the fore as a tractable mechanism for modeling asset returns. Exotic option values are especially sensitive to an accurate portrayal of these dynamics. This comprehensive volume provides a valuable service for financial researchers everywhere by assembling key contributions from the world's leading researchers in the field. Peter Carr, Head of Quantitative Finance, Bloomberg LP. This book provides a front-row seat to the hottest new field in modern finance: options pricing in turbulent markets. The old models have failed, as many a professional investor can sadly attest. So many of the brightest minds in mathematical finance across the globe are now in search of new, more accurate models. Here, in one volume, is a comprehensive selection of this cutting-edge research. Richard L. Hudson, former Managing Editor of The Wall Street Journal Europe, and co-author with Benoit B. Mandelbrot of The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward
Book Synopsis American-Type Options by : Dmitrii S. Silvestrov
Download or read book American-Type Options written by Dmitrii S. Silvestrov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-03-03 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematical presentation of stochastic approximation methods for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The volume presents results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.
Book Synopsis Ruin Probabilities by : S?ren Asmussen
Download or read book Ruin Probabilities written by S?ren Asmussen and published by World Scientific. This book was released on 2010 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Data Analysis and Related Applications 3 by : Yiannis Dimotikalis
Download or read book Data Analysis and Related Applications 3 written by Yiannis Dimotikalis and published by John Wiley & Sons. This book was released on 2024-05-21 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collective work by a number of leading scientists, analysts, engineers, mathematicians and statisticians who have been working at the forefront of data analysis and related applications, arising from data science, operations research, engineering, machine learning or statistics. The chapters of this collaborative work represent a cross-section of current research interests in the above scientific areas. The collected material has been divided into appropriate sections to provide the reader with both theoretical and applied information on data analysis methods, models and techniques, along with appropriate applications. The published data analysis methodology includes the updated state-of-the-art rapidly developed theory and applications of data expansion, both of which go through outstanding changes nowadays. New approaches are expected to deliver and have been developed, including Artificial Intelligence.
Book Synopsis Regime-switching Option Pricing Models by : Amalia Christoforidou
Download or read book Regime-switching Option Pricing Models written by Amalia Christoforidou and published by . This book was released on 2015 with total page 93 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Drawdowns by : Hongzhong Zhang
Download or read book Stochastic Drawdowns written by Hongzhong Zhang and published by World Scientific. This book was released on 2018-05-07 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic Drawdowns consists of some recent advances on Dr Hongzhong Zhang's own quantitative research of the well-known risk measures, drawdowns and maximum drawdowns. In this book, the author provides an extensive probabilistic study of different aspects of drawdown risks, which include the drawdown risk in finite time-horizons, the speed of market crashes (drawdowns), the frequency of drawdowns, the occupation time (time in distress), and the duration of drawdowns. Leveraging the knowledge in stochastic calculus, Lévy processes and optimal stopping, these topics can be considered as problems in advanced applied stochastic processes, and insurance/financial mathematics.The book also offers a number of applications of drawdowns in financial risk management, insurance, and algorithmic trading, including schemes on hedging and synthesizing of maximum drawdown options, (cancellable) drawdown insurance contracts and their fair premium, as well as optimal trading under drawdown-type constraints such as trailing stops.It is the goal of this book to offer a comprehensive characterization of drawdown risks and a handful of applications of drawdown in practice. On the one hand, the book enables interested students and researchers to learn the state-of-art probabilistic research on drawdowns, and explore new mathematical problems that are of practical importance to the financial industry. On the other hand, the book provides financial practitioners with access to a variety of analytically tractable measurements of drawdown risks, and the insight into hedging, optimal trading and execution amid challenges of these risks.
Book Synopsis Switching Levy Models in Continuous Time by : Kyriakos Chourdakis
Download or read book Switching Levy Models in Continuous Time written by Kyriakos Chourdakis and published by . This book was released on 2008 with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Hybrid Laplace Transform and Finite Difference Methods for Pricing American Options Under Complex Models by : Jingtang Ma
Download or read book Hybrid Laplace Transform and Finite Difference Methods for Pricing American Options Under Complex Models written by Jingtang Ma and published by . This book was released on 2017 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we propose a hybrid Laplace transform and finite difference method to price (finite-maturity) American options, which is applicable to a wide variety of asset price models including the constant elasticity of variance (CEV), hyper-exponential jump-diffusion (HEJD), Markov regime switching models, and the finite moment log stable (FMLS) models. We first apply Laplace transforms to free boundary partial differential equations (PDEs) or fractional partial differential equations (FPDEs) governing the American option prices with respect to time, and obtain second order ordinary differential equations (ODEs) or fractional differential equations (FDEs) with free boundary, which is named as the early exercise boundary in the American option pricing. Then, we develop an iterative algorithm based on finite difference methods to solve the ODEs or FDEs together with the unknown free boundary values in the Laplace space. Both the early exercise boundary and the prices of American options are recovered through inverse Laplace transforms. Numerical examples demonstrate the accuracy and efficiency of the method in CEV, HEJD, Markov regime switching models and the FMLS models.
Book Synopsis Advances in High Performance Computing by : Ivan Dimov
Download or read book Advances in High Performance Computing written by Ivan Dimov and published by Springer Nature. This book was released on 2020-08-07 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every day we need to solve large problems for which supercomputers are needed. High performance computing (HPC) is a paradigm that allows to efficiently implement large-scale computational tasks on powerful supercomputers unthinkable without optimization. We try to minimize our effort and to maximize the achieved profit. Many challenging real world problems arising in engineering, economics, medicine and other areas can be formulated as large-scale computational tasks. The volume is a comprehensive collection of extended contributions from the High performance computing conference held in Borovets, Bulgaria, September 2019. This book presents recent advances in high performance computing. The topics of interest included into this volume are: HP software tools, Parallel Algorithms and Scalability, HPC in Big Data analytics, Modelling, Simulation & Optimization in a Data Rich Environment, Advanced numerical methods for HPC, Hybrid parallel or distributed algorithms. The volume is focused on important large-scale applications like Environmental and Climate Modeling, Computational Chemistry and Heuristic Algorithms.
