Download or read book Pathwise Moderate Deviations for Option Pricing written by Antoine (Jack) Jacquier and published by . This book was released on 2018 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: We provide a unifying treatment of pathwise moderate deviations for models commonly used in financial applications, and for related integrated functionals. Suitable scaling allows us to transfer these results into small-time, large-time and tail asymptotics for diffusions, as well as for option prices and realised variances. In passing, we highlight some intuitive relationships between moderate deviations rate functions and their large deviations counterparts; these turn out to be useful for numerical purposes, as large deviations rate functions are often difficult to compute.
Download or read book Rough Volatility written by Christian Bayer and published by SIAM. This book was released on 2023-12-18 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volatility underpins financial markets by encapsulating uncertainty about prices, individual behaviors, and decisions and has traditionally been modeled as a semimartingale, with consequent scaling properties. The mathematical description of the volatility process has been an active topic of research for decades; however, driven by empirical estimates of the scaling behavior of volatility, a new paradigm has emerged, whereby paths of volatility are rougher than those of semimartingales. According to this perspective, volatility behaves essentially as a fractional Brownian motion with a small Hurst parameter. The first book to offer a comprehensive exploration of the subject, Rough Volatility contributes to the understanding and application of rough volatility models by equipping readers with the tools and insights needed to delve into the topic, exploring the motivation for rough volatility modeling, providing a toolbox for computation and practical implementation, and organizing the material to reflect the subject’s development and progression. This book is designed for researchers and graduate students in quantitative finance as well as quantitative analysts and finance professionals.
Download or read book Applications of Large Deviations Principles to Options Pricing and Portfolio Choice written by Scott Robertson and published by . This book was released on 2009 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract:The dissertation contains two parts. In each part, Large Deviations Principles (LDP) for diffusion processes are applied to problems from Mathematical Finance. Part I. In the Black-Scholes and Heston models, the problem is considered of selecting an Importance Sampling change of drift which minimizes the variance of Monte Carlo estimators for prices of path-dependent options. Employing Freidlin-Wentzell sample path LDP, an asymptotically optimal change of drift is identified as the solution to a variational problem, which may be reduced to the associated Euler-Lagrange differential equation. In the Black-Scholes model, closed-form solutions for geometric and arithmetic average Asian options are provided. In the Heston model, the case of the arithmetic average Asian put option is solved in detail. Since the Friedlin-Wentzell LDP results do not hold in the Heston model, sample path LDP are derived for a class of diffusion processes allowed to have a non-locally Lipschitz diffusion matrix. Such results lead to sample path LDP for the price process in the Heston and Hull & White models. Part II. For an investor with power utility and in the limit of a long horizon, a method is developed to derive optimal portfolios and risk premia explicitly in a general diffusion model. Investment opportunities are driven by state variables which follow an autonomous diffusion. Using occupation time distribution LDP for Markov processes, long-run portfolios and risk premia admit explicit formulas up to the solution of a semi-linear ordinary differential equation which linearizes in the case of one state variable. Finite horizon performance of the long-run portfolio and risk-premia is also derived. In the case of one state variable, optimal portfolios and risk-premia are derived for all time horizons up to the solution of a linear evolution equation. In the absence of a continuous spectrum, a candidate solution is obtained via an eigenfunction expansion. Portfolios and risk premia converge to their long-run counterparts as the horizon becomes large. Applications to cross-sectional models with predictability, stochastic volatility and stochastic interest rates conclude both the long-run and finite horizon sections.
Download or read book Option Volatility Pricing Advanced Trading Strategies and Techniques written by Sheldon Natenberg and published by McGraw Hill Professional. This book was released on 1994-08 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a thorough discussion of volatility, the most important aspect of options trading. Shows how to identify mispriced options and to construct volatility and "delta neutral" spreads.
Download or read book Metastability written by Anton Bovier and published by Springer. This book was released on 2016-02-11 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a concise presentation of a mathematical approach to metastability, a wide-spread phenomenon in the dynamics of non-linear systems - physical, chemical, biological or economic - subject to the action of temporal random forces typically referred to as noise, based on potential theory of reversible Markov processes. The authors shed new light on the metastability phenomenon as a sequence of visits of the path of the process to different metastable sets, and focuses on the precise analysis of the respective hitting probabilities and hitting times of these sets. The theory is illustrated with many examples, ranging from finite-state Markov chains, finite-dimensional diffusions and stochastic partial differential equations, via mean-field dynamics with and without disorder, to stochastic spin-flip and particle-hop dynamics and probabilistic cellular automata, unveiling the common universal features of these systems with respect to their metastable behaviour. The monograph will serve both as comprehensive introduction and as reference for graduate students and researchers interested in metastability.
Download or read book Large Deviations and Metastability written by Enzo Olivieri and published by Cambridge University Press. This book was released on 2005-02-21 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
Download or read book Mathematical Methods for Financial Markets written by Monique Jeanblanc and published by Springer Science & Business Media. This book was released on 2009-10-03 with total page 754 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical finance has grown into a huge area of research which requires a large number of sophisticated mathematical tools. This book simultaneously introduces the financial methodology and the relevant mathematical tools in a style that is mathematically rigorous and yet accessible to practitioners and mathematicians alike. It interlaces financial concepts such as arbitrage opportunities, admissible strategies, contingent claims, option pricing and default risk with the mathematical theory of Brownian motion, diffusion processes, and Lévy processes. The first half of the book is devoted to continuous path processes whereas the second half deals with discontinuous processes. The extensive bibliography comprises a wealth of important references and the author index enables readers quickly to locate where the reference is cited within the book, making this volume an invaluable tool both for students and for those at the forefront of research and practice.
Download or read book A Course on Rough Paths written by Peter K. Friz and published by Springer Nature. This book was released on 2020-05-27 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: With many updates and additional exercises, the second edition of this book continues to provide readers with a gentle introduction to rough path analysis and regularity structures, theories that have yielded many new insights into the analysis of stochastic differential equations, and, most recently, stochastic partial differential equations. Rough path analysis provides the means for constructing a pathwise solution theory for stochastic differential equations which, in many respects, behaves like the theory of deterministic differential equations and permits a clean break between analytical and probabilistic arguments. Together with the theory of regularity structures, it forms a robust toolbox, allowing the recovery of many classical results without having to rely on specific probabilistic properties such as adaptedness or the martingale property. Essentially self-contained, this textbook puts the emphasis on ideas and short arguments, rather than aiming for the strongest possible statements. A typical reader will have been exposed to upper undergraduate analysis and probability courses, with little more than Itô-integration against Brownian motion required for most of the text. From the reviews of the first edition: "Can easily be used as a support for a graduate course ... Presents in an accessible way the unique point of view of two experts who themselves have largely contributed to the theory" - Fabrice Baudouin in the Mathematical Reviews "It is easy to base a graduate course on rough paths on this ... A researcher who carefully works her way through all of the exercises will have a very good impression of the current state of the art" - Nicolas Perkowski in Zentralblatt MATH
Download or read book Large Deviations and Asymptotic Methods in Finance written by Peter K. Friz and published by Springer. This book was released on 2015-06-16 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find this book very useful, and the diversity of topics will appeal to people from mathematical finance, probability theory and differential geometry.
Download or read book Machine Learning and Knowledge Discovery in Databases Applied Data Science and Demo Track written by Gianmarco De Francisci Morales and published by Springer Nature. This book was released on with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Large Deviations for Stochastic Processes written by Jin Feng and published by American Mathematical Soc.. This book was released on 2006 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the results on large deviations for a class of stochastic processes. Following an introduction and overview, the material is presented in three parts. Part 1 gives necessary and sufficient conditions for exponential tightness that are analogous to conditions for tightness in the theory of weak convergence. Part 2 focuses on Markov processes in metric spaces. For a sequence of such processes, convergence of Fleming's logarithmically transformed nonlinear semigroups is shown to imply the large deviation principle in a manner analogous to the use of convergence of linear semigroups in weak convergence. Viscosity solution methods provide applicable conditions for the necessary convergence. Part 3 discusses methods for verifying the comparison principle for viscosity solutions and applies the general theory to obtain a variety of new and known results on large deviations for Markov processes. In examples concerning infinite dimensional state spaces, new comparison principles are de
Download or read book Large Deviations and the Malliavin Calculus written by Jean-Michel Bismut and published by Birkhäuser. This book was released on 1984 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Methods and Finance written by Emiliano Ippoliti and published by Springer. This book was released on 2016-12-23 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book offers an interdisciplinary perspective on finance, with a special focus on stock markets. It presents new methodologies for analyzing stock markets’ behavior and discusses theories and methods of finance from different angles, such as the mathematical, physical and philosophical ones. The book, which aims at philosophers and economists alike, represents a rare yet important attempt to unify the externalist with the internalist conceptions of finance.
Download or read book The Fair Value of Insurance Business written by Irwin T. Vanderhoof and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Insurance companies, as well as banks and thrift institutions, have traditionally reported assets and liabilities on the basis of their amortized cost, or book value. But following the turmoil in securities markets due to highly volatile interest rate fluctuations in the 1980s and the early 1990s, and problems caused by inadequate liquidity, in the mid-1990s the Financial Accounting Standards Board (FASB) issued a new ruling calling for financial intermediaries to report the fair, or market, value of most assets. Called FAS 115, this new standard is the first step in the eventual change to valuing all the assets and liabilities belonging to financial intermediaries under the fair value accounting method. Thus, these changes will pose tremendous future implications for three key business measures of a financial intermediary: Solvency: if the fair values of assets and liabilities are out-of-step, then healthy companies may report negative net worth and insolvent companies may appear to be in sound financial condition. Reported Earnings: if the fair values of assets and liabilities are out of step, then reported earnings will not accurately represent the financial operations of the company. Risk Management: FASB recently postponed the implementation of its new rules on accounting for the use of derivatives instruments. However, if the final set of rules for figuring the fair value of derivatives is not carefully crafted, it may be possible that companies prudently hedging their risks are subject to penalties in their financial reports, while companies taking greater risks appear to have less volatile financial performance. Compared to banks and other financial intermediaries, life insurance companies have the longest term and most complex liabilities, and hence the new FASB requirement poses the most severe challenges to the life insurance industry. The lessons learned from the debate among life insurance academics and professionals about how respond to the fair value reporting rule will be instructive to their counterparts in other sectors of the insurance industry, as well as those involved with other financial institutions. Of particular note are the two papers which comprise Part III. The first provides examples of the fair valuing of annuity contracts, while the second offers examples of the fair valuing of term insurance products. As the papers collected in The Fair Value of Insurance Business extend and update some of the issues treated in a previous Salomon Center conference volume, The Fair Value of Insurance Liabilities, this new volume may be viewed as a companion to the earlier book.
Download or read book Theory of Financial Risk and Derivative Pricing written by Jean-Philippe Bouchaud and published by Cambridge University Press. This book was released on 2003-12-11 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded. Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game. There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models. This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies.
Download or read book The Greeks and Hedging Explained written by Peter Leoni and published by Springer. This book was released on 2014-05-29 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical guide to basic and intermediate hedging techniques for traders, structerers and risk management quants. This book fills a gap for a technical but not impenetrable guide to hedging options, and the 'Greek' (Theta, Vega, Rho and Lambda) -parameters that represent the sensitivity of derivatives prices.
Download or read book Neural Fields written by Stephen Coombes and published by Springer. This book was released on 2014-06-17 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neural field theory has a long-standing tradition in the mathematical and computational neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan, Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Robinson, Bressloff, Wright and Haken. Since then, much progress has been made in both, the development of mathematical and numerical techniques and in physiological refinement und understanding. In contrast to large-scale neural network models described by huge connectivity matrices that are computationally expensive in numerical simulations, neural field models described by connectivity kernels allow for analytical treatment by means of methods from functional analysis. Thus, a number of rigorous results on the existence of bump and wave solutions or on inverse kernel construction problems are nowadays available. Moreover, neural fields provide an important interface for the coupling of neural activity to experimentally observable data, such as the electroencephalogram (EEG) or functional magnetic resonance imaging (fMRI). And finally, neural fields over rather abstract feature spaces, also called dynamic fields, found successful applications in the cognitive sciences and in robotics. Up to now, research results in neural field theory have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. There is no comprehensive collection of results or reviews available yet. With our proposed book Neural Field Theory, we aim at filling this gap in the market. We received consent from some of the leading scientists in the field, who are willing to write contributions for the book, among them are two of the founding-fathers of neural field theory: Shun-ichi Amari and Jack Cowan.
