In this paper we primarily obtain the explicit formulas for the distribution function of the variance gamma process. The formulas are based on values of hypergeometric functions. This result is applied to European option pricing. Basing on the established formulas, we get the prices of binary options, as long as the price of European call which was derived firstly in paper by Madan, Carr and Chang (1998).
Inspired by the Encyclopedia of Statistical Sciences, Second Edition, this volume presents the tools and techniques that are essential for carrying out best practices in the modern business world The collection and analysis of quantitative data drives some of the most important conclusions that are drawn in today's business world, such as the preferences of a customer base, the quality of manufactured products, the marketing of products, and the availability of financial resources. As a result, it is essential for individuals working in this environment to have the knowledge and skills to interpret and use statistical techniques in various scenarios. Addressing this need, Methods and Applications of Statistics in Business, Finance, and Management Science serves as a single, one-of-a-kind resource that guides readers through the use of common statistical practices by presenting real-world applications from the fields of business, economics, finance, operations research, and management science. Uniting established literature with the latest research, this volume features classic articles from the acclaimed Encyclopedia of Statistical Sciences, Second Edition along with brand-new contributions written by today's leading academics and practitioners. The result is a compilation that explores classic methodology and new topics, including: Analytical methods for risk management Statistical modeling for online auctions Ranking and selection in mutual funds Uses of Black-Scholes formula in finance Data mining in prediction markets From auditing and marketing to stock market price indices and banking, the presented literature sheds light on the use of quantitative methods in research relating to common financial applications. In addition, the book supplies insight on common uses of statistical techniques such as Bayesian methods, optimization, simulation, forecasting, mathematical modeling, financial time series, and data mining in modern research. Providing a blend of traditional methodology and the latest research, Methods and Applications of Statistics in Business, Finance, and Management Science is an excellent reference for researchers, managers, consultants, and students in the fields of business, management science, operations research, supply chain management, mathematical finance, and economics who must understand statistical literature and carry out quantitative practices to make smart business decisions in their everyday work.
A problem of risk neutral probability density function estimation for prices of risky assets is discussed when the asset pricing model uses exponential random process with independent increments. The structure of increments consists of two components: systematic drift and a random gamma distributed component. To determine the risk neutral probability density Escher transform is used. Obtained results help to define a formula for European call option pricing. Also we compare the found risk neutral density with the density, when the random component is defined by a Wiener process, driven by gamma process.
This book addresses the applications of Fourier transform to smile modeling. Smile effect is used generically by ?nancial engineers and risk managers to refer to the inconsistences of quoted implied volatilities in ?nancial markets, or more mat- matically, to the leptokurtic distributions of ?nancial assets and indices. Therefore, a sound modeling of smile effect is the central challenge in quantitative ?nance. Since more than one decade, Fourier transform has triggered a technical revolution in option pricing theory. Almost all new developed option pricing models, es- cially in connection with stochastic volatility and random jump, have extensively applied Fourier transform and the corresponding inverse transform to express - tion pricing formulas. The large accommodation of the Fourier transform allows for a very convenient modeling with a general class of stochastic processes and d- tributions. This book is then intended to present a comprehensive treatment of the Fourier transform in the option valuation, covering the most stochastic factors such as stochastic volatilities and interest rates, Poisson and Levy ́ jumps, including some asset classes such as equity, FX and interest rates, and providing numerical ex- ples and prototype programming codes. I hope that readers will bene?t from this book not only by gaining an overview of the advanced theory and the vast large l- erature on these topics, but also by gaining a ?rst-hand feedback from the practice on the applications and implementations of the theory.
This book gathers contributions presented at the 10th Workshop on Cyclostationary Systems and Their Applications, held in Gródek nad Dunajcem, Poland in February 2017. It includes twelve interesting papers covering current topics related to both cyclostationary and general non stationary processes. Moreover, this book, which covers both theoretical and practical issues, offers a practice-oriented guide to the analysis of data sets with non-stationary behavior and a bridge between basic and applied research on nonstationary processes. It provides students, researchers and professionals with a timely guide on cyclostationary systems, nonstationary processes and relevant engineering applications.
This handbook includes contributions related to optimization, pricing and valuation problems, risk modeling and decision making problems arising in global financial and commodity markets from the perspective of Operations Research and Management Science. The book is structured in three parts, emphasizing common methodological approaches arising in the areas of interest: - Part I: Optimization techniques - Part II: Pricing and Valuation - Part III: Risk Modeling The book presents to a wide community of Academics and Practitioners a selection of theoretical and applied contributions on topics that have recently attracted increasing interest in commodity and financial markets. Within a structure based on the three parts, it presents recent state-of-the-art and original works related to: - The adoption of multi-criteria and dynamic optimization approaches in financial and insurance markets in presence of market stress and growing systemic risk; - Decision paradigms, based on behavioral finance or factor-based, or more classical stochastic optimization techniques, applied to portfolio selection problems including new asset classes such as alternative investments; - Risk measurement methodologies, including model risk assessment, recently applied to energy spot and future markets and new risk measures recently proposed to evaluate risk-reward trade-offs in global financial and commodity markets; and derivatives portfolio hedging and pricing methods recently put forward in the financial community in the aftermath of the global financial crisis.
