change of time methods in quantitative finance

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Change Of Time Methods In Quantitative Finance

Author : Anatoliy Swishchuk
ISBN : 9783319324081
Genre : Mathematics
File Size : 87. 74 MB
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This book is devoted to the history of Change of Time Methods (CTM), the connections of CTM to stochastic volatilities and finance, fundamental aspects of the theory of CTM, basic concepts, and its properties. An emphasis is given on many applications of CTM in financial and energy markets, and the presented numerical examples are based on real data. The change of time method is applied to derive the well-known Black-Scholes formula for European call options, and to derive an explicit option pricing formula for a European call option for a mean-reverting model for commodity prices. Explicit formulas are also derived for variance and volatility swaps for financial markets with a stochastic volatility following a classical and delayed Heston model. The CTM is applied to price financial and energy derivatives for one-factor and multi-factor alpha-stable Levy-based models. Readers should have a basic knowledge of probability and statistics, and some familiarity with stochastic processes, such as Brownian motion, Levy process and martingale.

Time Change Method In Quantitative Finance

Author : Zhenyu Cui
ISBN : OCLC:827743718
Genre :
File Size : 64. 69 MB
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In this thesis I discuss the method of time-change and its applications in quantitative finance. I mainly consider the time change by writing a continuous diffusion process as a Brownian motion subordinated by a subordinator process. I divide the time change method into two cases: deterministic time change and stochastic time change. The difference lies in whether the subordinator process is a deterministic function of time or a stochastic process of time. Time-changed Brownian motion with deterministic time change provides a new viewpoint to deal with option pricing under stochastic interest rates and I utilize this idea in pricing various exotic options under stochastic interest rates. Time-changed Brownian motion with stochastic time change is more complicated and I give the equivalence in law relation governing the "original time" and the "new stochastic time" under different clocks. This is readily applicable in pricing a new product called "timer option". It can also be used in pricing barrier options under the Heston stochastic volatility model. Conclusion and further research directions in exploring the ideas of time change method in other areas of quantitative finance are in the last chapter.

Implementing Models In Quantitative Finance Methods And Cases

Author : Gianluca Fusai
ISBN : 3540499598
Genre : Business & Economics
File Size : 69. 83 MB
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This book puts numerical methods in action for the purpose of solving practical problems in quantitative finance. The first part develops a toolkit in numerical methods for finance. The second part proposes twenty self-contained cases covering model simulation, asset pricing and hedging, risk management, statistical estimation and model calibration. Each case develops a detailed solution to a concrete problem arising in applied financial management and guides the user towards a computer implementation. The appendices contain "crash courses" in VBA and Matlab programming languages.

Applied Quantitative Finance

Author : Wolfgang Härdle
ISBN : 9783540691792
Genre : Mathematics
File Size : 66. 89 MB
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Recent years have witnessed a growing importance of quantitative methods in both financial research and industry. This development requires the use of advanced techniques on a theoretical and applied level, especially when it comes to the quantification of risk and the valuation of modern financial products. Applied Quantitative Finance (2nd edition) provides a comprehensive and state-of-the-art treatment of cutting-edge topics and methods. It provides solutions to and presents theoretical developments in many practical problems such as risk management, pricing of credit derivatives, quantification of volatility and copula modelling. The synthesis of theory and practice supported by computational tools is reflected in the selection of topics as well as in a finely tuned balance of scientific contributions on practical implementation and theoretical concepts. This linkage between theory and practice offers theoreticians insights into considerations of applicability and, vice versa, provides practitioners comfortable access to new techniques in quantitative finance. Themes that are dominant in current research and which are presented in this book include among others the valuation of Collaterized Debt Obligations (CDOs), the high-frequency analysis of market liquidity, the pricing of Bermuda options and realized volatility. All Quantlets for the calculation of the given examples are downloadable from the Springer web pages.

Quantitative Finance And Risk Management

Author : Jan W Dash
ISBN : 9789814571258
Genre : Business & Economics
File Size : 82. 9 MB
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Written by a physicist with extensive experience as a risk/finance quant, this book treats a wide variety of topics. Presenting the theory and practice of quantitative finance and risk, it delves into the "how to" and "what it's like" aspects not covered in textbooks or papers. A "Technical Index" indicates the mathematical level for each chapter. This second edition includes some new, expanded, and wide-ranging considerations for risk management: Climate Change and its long-term systemic risk; Markets in Crisis and the Reggeon Field Theory; "Smart Monte Carlo" and American Monte Carlo; Trend Risk — time scales and risk, the Macro–Micro model, singular spectrum analysis; credit risk: counterparty risk and issuer risk; stressed correlations — new techniques; and Psychology and option models. Solid risk management topics from the first edition and valid today are included: standard/advanced theory and practice in fixed income, equities, and FX; quantitative finance and risk management — traditional/exotic derivatives, fat tails, advanced stressed VAR, model risk, numerical techniques, deals/portfolios, systems, data, economic capital, and a function toolkit; risk lab — the nuts and bolts of risk management from the desk to the enterprise; case studies of deals; Feynman path integrals, Green functions, and options; and "Life as a Quant" — communication issues, sociology, stories, and advice.

Copulae In Mathematical And Quantitative Finance

Author : Piotr Jaworski
ISBN : 9783642354076
Genre : Business & Economics
File Size : 76. 89 MB
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Copulas are mathematical objects that fully capture the dependence structure among random variables and hence offer great flexibility in building multivariate stochastic models. Since their introduction in the early 1950s, copulas have gained considerable popularity in several fields of applied mathematics, especially finance and insurance. Today, copulas represent a well-recognized tool for market and credit models, aggregation of risks, and portfolio selection. Historically, the Gaussian copula model has been one of the most common models in credit risk. However, the recent financial crisis has underlined its limitations and drawbacks. In fact, despite their simplicity, Gaussian copula models severely underestimate the risk of the occurrence of joint extreme events. Recent theoretical investigations have put new tools for detecting and estimating dependence and risk (like tail dependence, time-varying models, etc) in the spotlight. All such investigations need to be further developed and promoted, a goal this book pursues. The book includes surveys that provide an up-to-date account of essential aspects of copula models in quantitative finance, as well as the extended versions of talks selected from papers presented at the workshop in Cracow.

Quantitative Finance

Author : Erik Schlogl
ISBN : 9781498785549
Genre : Mathematics
File Size : 73. 9 MB
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Quantitative Finance: An Object-Oriented Approach in C++ provides readers with a foundation in the key methods and models of quantitative finance. Keeping the material as self-contained as possible, the author introduces computational finance with a focus on practical implementation in C++. Through an approach based on C++ classes and templates, the text highlights the basic principles common to various methods and models while the algorithmic implementation guides readers to a more thorough, hands-on understanding. By moving beyond a purely theoretical treatment to the actual implementation of the models using C++, readers greatly enhance their career opportunities in the field. The book also helps readers implement models in a trading or research environment. It presents recipes and extensible code building blocks for some of the most widespread methods in risk management and option pricing. Web Resource The author’s website provides fully functional C++ code, including additional C++ source files and examples. Although the code is used to illustrate concepts (not as a finished software product), it nevertheless compiles, runs, and deals with full, rather than toy, problems. The website also includes a suite of practical exercises for each chapter covering a range of difficulty levels and problem complexity.

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