Modeling And Pricing Of Swaps For Financial And Energy Markets With Stochastic Volatilities

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. Contents:Stochastic VolatilityStochastic Volatility ModelsSwapsChange of Time MethodsBlack-Scholes Formula by Change of Time MethodModeling and Pricing of Swaps for Heston ModelModeling and Pricing of Variance Swaps for Stochastic Volatilities with DelayModeling and Pricing of Variance Swaps for Multi-Factor Stochastic Volatilities with DelayPricing Variance Swaps for Stochastic Volatilities with Delay and JumpsVariance Swap for Local Lévy-Based Stochastic Volatility with DelayDelayed Heston Model: Improvement of the Volatility Surface FittingPricing and Hedging of Volatility Swap in the Delayed Heston ModelPricing of Variance and Volatility Swaps with Semi-Markov VolatilitiesCovariance and Correlation Swaps for Markov-Modulated VolatilitiesVolatility and Variance Swaps for the COGARCH(1,1) ModelVariance and Volatility Swaps for Volatilities Driven by Fractional Brownian MotionVariance and Volatility Swaps in Energy MarketsExplicit Option Pricing Formula for a Mean-Reverting Asset in Energy MarketsForward and Futures in Energy Markets: Multi-Factor Lévy ModelsGeneralization of Black-76 Formula: Markov-Modulated Volatility Readership: Post-graduate level researchers and professionals with interest in the modeling and pricing of swaps for energy and financial markets. Keywords:Stochastic Volatilities;Variance, Volatility, Covariance, Correlation Swaps;Change of Time;Option Pricing;Stochastic Volatilities with Delay;Multi-Factor Stochastic Volatilities Models;Regime-Switching Stochastic Volatilities;Levy-Based Stochastic Volatilities with Delay;COGARCH Stochastic Volatility;Stochastic Volatility Driven by Fractional Brownian Motion;Delayed Heston Model;Semi-Markov Stochastic Volatilities;Energy Markets;Forward and Futures in Energy MarketsKey Features:Provides coverage on topic of swaps not covered in such detail by other titles, in relation to energy and financial marketsIn particular, offers a comprehensive treatment of various types of swaps and a variety of stochastic volatility models, in relation to energy and financial marketsReviews: “A separate session about the derivative pricing on the energy market is included. Moreover, this book provides many numerical examples to illustrate applications of the stochastic volatility pricing models. This book is quite useful not only for academics and researchers in mathematical and energy finance, but also for practitioners in the financial and energy industries.” Zentralblatt MATH

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.

The markets for electricity, gas and temperature have distinctive features, which provide the focus for countless studies. For instance, electricity and gas prices may soar several magnitudes above their normal levels within a short time due to imbalances in supply and demand, yielding what is known as spikes in the spot prices. The markets are also largely influenced by seasons, since power demand for heating and cooling varies over the year. The incompleteness of the markets, due to nonstorability of electricity and temperature as well as limited storage capacity of gas, makes spot-forward hedging impossible. Moreover, futures contracts are typically settled over a time period rather than at a fixed date. All these aspects of the markets create new challenges when analyzing price dynamics of spot, futures and other derivatives.This book provides a concise and rigorous treatment on the stochastic modeling of energy markets. Ornstein?Uhlenbeck processes are described as the basic modeling tool for spot price dynamics, where innovations are driven by time-inhomogeneous jump processes. Temperature futures are studied based on a continuous higher-order autoregressive model for the temperature dynamics. The theory presented here pays special attention to the seasonality of volatility and the Samuelson effect. Empirical studies using data from electricity, temperature and gas markets are given to link theory to practice.

An essential reference dedicated to a wide array of financial models, issues in financial modeling, and mathematical and statistical tools for financial modeling The need for serious coverage of financial modeling has never been greater, especially with the size, diversity, and efficiency of modern capital markets. With this in mind, the Encyclopedia of Financial Models, 3 Volume Set has been created to help a broad spectrum of individuals—ranging from finance professionals to academics and students—understand financial modeling and make use of the various models currently available. Incorporating timely research and in-depth analysis, the Encyclopedia of Financial Models is an informative 3-Volume Set that covers both established and cutting-edge models and discusses their real-world applications. Edited by Frank Fabozzi, this set includes contributions from global financial experts as well as academics with extensive consulting experience in this field. Organized alphabetically by category, this reliable resource consists of three separate volumes and 127 entries—touching on everything from asset pricing and bond valuation models to trading cost models and volatility—and provides readers with a balanced understanding of today's dynamic world of financial modeling. Frank Fabozzi follows up his successful Handbook of Finance with another major reference work, The Encyclopedia of Financial Models Covers the two major topical areas: asset valuation for cash and derivative instruments, and portfolio modeling Fabozzi explores the critical background tools from mathematics, probability theory, statistics, and operations research needed to understand these complex models Organized alphabetically by category, this book gives readers easy and quick access to specific topics sorted by an applicable category among them Asset Allocation, Credit Risk Modeling, Statistical Tools 3 Volumes onlinelibrary.wiley.com Financial models have become increasingly commonplace, as well as complex. They are essential in a wide range of financial endeavors, and this 3-Volume Set will help put them in perspective.

Volume 1 of the Encyclopedia of Financial Models The need for serious coverage of financial modeling has never been greater, especially with the size, diversity, and efficiency of modern capital markets. With this in mind, the Encyclopedia of Financial Models has been created to help a broad spectrum of individuals ranging from finance professionals to academics and students understand financial modeling and make use of the various models currently available. Incorporating timely research and in-depth analysis, Volume 1 of the Encyclopedia of Financial Models covers both established and cutting-edge models and discusses their real-world applications. Edited by Frank Fabozzi, this volume includes contributions from global financial experts as well as academics with extensive consulting experience in this field. Organized alphabetically by category, this reliable resource consists of thirty-nine informative entries and provides readers with a balanced understanding of today's dynamic world of financial modeling. Volume 1 addresses Asset Pricing Models, Bayesian Analysis and Financial Modeling Applications, Bond Valuation Modeling, Credit Risk Modeling, and Derivatives Valuation Emphasizes both technical and implementation issues, providing researchers, educators, students, and practitioners with the necessary background to deal with issues related to financial modeling The 3-Volume Set contains coverage of the fundamentals and advances in financial modeling and provides the mathematical and statistical techniques needed to develop and test financial models Financial models have become increasingly commonplace, as well as complex. They are essential in a wide range of financial endeavors, and the Encyclopedia of Financial Models will help put them in perspective.

Pricing Models of Volatility Products and Exotic Variance Derivatives summarizes most of the recent research results in pricing models of derivatives on discrete realized variance and VIX. The book begins with the presentation of volatility trading and uses of variance derivatives. It then moves on to discuss the robust replication strategy of variance swaps using portfolio of options, which is one of the major milestones in pricing theory of variance derivatives. The replication procedure provides the theoretical foundation of the construction of VIX. This book provides sound arguments for formulating the pricing models of variance derivatives and establishes formal proofs of various technical results. Illustrative numerical examples are included to show accuracy and effectiveness of analytic and approximation methods. Features Useful for practitioners and quants in the financial industry who need to make choices between various pricing models of variance derivatives Fabulous resource for researchers interested in pricing and hedging issues of variance derivatives and VIX products Can be used as a university textbook in a topic course on pricing variance derivatives

Written by leading market risk academic, Professor Carol Alexander, Pricing, Hedging and Trading Financial Instruments forms part three of the Market Risk Analysis four volume set. This book is an in-depth, practical and accessible guide to the models that are used for pricing and the strategies that are used for hedging financial instruments, and to the markets in which they trade. It provides a comprehensive, rigorous and accessible introduction to bonds, swaps, futures and forwards and options, including variance swaps, volatility indices and their futures and options, to stochastic volatility models and to modelling the implied and local volatility surfaces. All together, the Market Risk Analysis four volume set illustrates virtually every concept or formula with a practical, numerical example or a longer, empirical case study. Across all four volumes there are approximately 300 numerical and empirical examples, 400 graphs and figures and 30 case studies many of which are contained in interactive Excel spreadsheets available from the the accompanying CD-ROM . Empirical examples and case studies specific to this volume include: Duration-Convexity approximation to bond portfolios, and portfolio immunization; Pricing floaters and vanilla, basis and variance swaps; Coupon stripping and yield curve fitting; Proxy hedging, and hedging international securities and energy futures portfolios; Pricing models for European exotics, including barriers, Asians, look-backs, choosers, capped, contingent, power, quanto, compo, exchange, ‘best-of’ and spread options; Libor model calibration; Dynamic models for implied volatility based on principal component analysis; Calibration of stochastic volatility models (Matlab code); Simulations from stochastic volatility and jump models; Duration, PV01 and volatility invariant cash flow mappings; Delta-gamma-theta-vega mappings for options portfolios; Volatility beta mapping to volatility indices.

This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.