Download or read book Analytic Pricing of Volatility Equity Options Within Affine Models written by José Da Fonseca and published by . This book was released on 2015 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: We price for different affine stochastic volatility models some derivatives that recently appeared in the market. These products are characterised by payoffs depending on both stock and its volatility. Using a Fourier-analysis approach, we recover in a much simpler way some results already established in the literature for the single factor specification of the volatility and we push forward our methodology, which turns out to be independent of the dimension of the problem, thanks to a simple conditioning with respect to the subfiltration generated by the variance path. For each product we provide a closed form solution based on the Fast Fourier Transform and we illustrate the results for realistic model parameter values. Also, our results highlight the great flexibility and tractability of the Wishart based stochastic volatility models.
Download or read book Pricing Models of Volatility Products and Exotic Variance Derivatives written by Yue Kuen Kwok and published by CRC Press. This book was released on 2022-05-08 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Analytic Equity Option Pricing with Stochastic Volatility written by Colin Turfus and published by . This book was released on 2020 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the Heston stochastic volatility model for equity options and use operator formalism and perturbation expansion techniques to derive a formal analytic expression for the Green's function (pricing kernel). This is expanded explicitly as a perturbation series in powers of the vol of vol up to second order and used to obtain an asymptotically accurate pricing formula for vanilla equity options, replicating results obtained previously by Ito and Malliavin techniques.
Download or read book Analytically Tractable Stochastic Stock Price Models written by Archil Gulisashvili and published by Springer Science & Business Media. This book was released on 2012-09-04 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic analysis of stochastic stock price models is the central topic of the present volume. Special examples of such models are stochastic volatility models, that have been developed as an answer to certain imperfections in a celebrated Black-Scholes model of option pricing. In a stock price model with stochastic volatility, the random behavior of the volatility is described by a stochastic process. For instance, in the Hull-White model the volatility process is a geometric Brownian motion, the Stein-Stein model uses an Ornstein-Uhlenbeck process as the stochastic volatility, and in the Heston model a Cox-Ingersoll-Ross process governs the behavior of the volatility. One of the author's main goals is to provide sharp asymptotic formulas with error estimates for distribution densities of stock prices, option pricing functions, and implied volatilities in various stochastic volatility models. The author also establishes sharp asymptotic formulas for the implied volatility at extreme strikes in general stochastic stock price models. The present volume is addressed to researchers and graduate students working in the area of financial mathematics, analysis, or probability theory. The reader is expected to be familiar with elements of classical analysis, stochastic analysis and probability theory.
Download or read book Option Pricing for an Affine Jump Diffusion Model written by Zhiqiu Li and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first part of this thesis, we study the asymptotic behaviors of implied volatility of an affine jump-diffusion (AJD) model. Let log stock price under risk-neutral measure follow an AJD model, we show that an explicit form of moment generating function for log stock price can be obtained by solving a set of ordinary differential equations. A large-time large deviation principle for log stock price is derived by applying the G\"{a}rtner-Ellis theorem. We characterize the asymptotic behaviors of the implied volatility in the large-maturity and large-strike regime using rate function in the large deviation principle. The asymptotics of the Black-Scholes implied volatility for fixed-maturity, large-strike and fixed-maturity, small-strike regimes are also studied. Numerical results are provided to validate the theoretical work. In the second part of this thesis, we study the European option pricing problem when the underlying stock follows an AJD model whose jump interarrival time has a Cox-Ingersoll-Ross type intensity dynamics. An analytic formula of a European option pricing is derived using the Fourier inversion transform technique. We develop a Monte Carlo algorithm to simulate the dynamics of an AJD model. We observe AJD At-The-Money (ATM) European option prices using the Monte Carlo simulation converge to the Fourier analytic ones as the number of simulation paths increases.
Download or read book Transform Analysis and Asset Pricing for Affine Jump diffusions written by Darrell Duffie and published by . This book was released on 1999 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the setting of affine' jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensityy-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option 'smirks' of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both amplitude as well as jump timing.
Download or read book Pricing Models of Volatility Products and Exotic Variance Derivatives written by Yue Kuen Kwok and published by CRC Press. This book was released on 2022-05-08 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Option Pricing Models and Volatility Using Excel VBA written by Fabrice D. Rouah and published by John Wiley & Sons. This book was released on 2012-06-15 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive guide offers traders, quants, and students the tools and techniques for using advanced models for pricing options. The accompanying website includes data files, such as options prices, stock prices, or index prices, as well as all of the codes needed to use the option and volatility models described in the book. Praise for Option Pricing Models & Volatility Using Excel-VBA "Excel is already a great pedagogical tool for teaching option valuation and risk management. But the VBA routines in this book elevate Excel to an industrial-strength financial engineering toolbox. I have no doubt that it will become hugely successful as a reference for option traders and risk managers." —Peter Christoffersen, Associate Professor of Finance, Desautels Faculty of Management, McGill University "This book is filled with methodology and techniques on how to implement option pricing and volatility models in VBA. The book takes an in-depth look into how to implement the Heston and Heston and Nandi models and includes an entire chapter on parameter estimation, but this is just the tip of the iceberg. Everyone interested in derivatives should have this book in their personal library." —Espen Gaarder Haug, option trader, philosopher, and author of Derivatives Models on Models "I am impressed. This is an important book because it is the first book to cover the modern generation of option models, including stochastic volatility and GARCH." —Steven L. Heston, Assistant Professor of Finance, R.H. Smith School of Business, University of Maryland
Download or read book Characteristic Function Based Estimation of Affine Option Pricing Models written by Yannick Dillschneider and published by . This book was released on 2019 with total page 12 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we derive explicit expressions for certain joint moments of stock prices and option prices within a generic affine stochastic volatility model. Evaluation of each moment requires weighted inverse Fourier transformation of a function that is determined by the risk-neutral and real-world characteristic functions of the state vector. Explicit availability of such moment expressions allows to devise a novel GMM approach to jointly estimate real-world and risk-neutral parameters of affine stochastic volatility models using observed individual option prices. Moreover, the moment expressions may be used to include option price information into other existing moment-based estimation approaches.
Download or read book Essays on Empirical Performance of Affine Jump diffusion Option Pricing Models written by Xiang Zhang and published by . This book was released on 2012 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic volatility and the pricing of financial derivatives written by Antoine Petrus Cornelius van der Ploeg and published by Rozenberg Publishers. This book was released on 2006 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Efficient pricing algorithms for exotic derivatives written by Roger Lord and published by Rozenberg Publishers. This book was released on 2008 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book VIX Option Pricing Under Volatility Affine Models written by 林明賢 and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Analysis Of Stochastic Volatility Jump Diffusion Models written by Abdelilah Jraifi and published by LAP Lambert Academic Publishing. This book was released on 2014-06-30 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the modern economic world, the options contracts are used because they allow to hedge against the vagaries and risks refers to fluctuations in the prices of the underlying assets. The determination of the price of these contracts is of great importance for investors.We are interested in problems of options pricing, actually the European and Quanto options on a financial asset. The price of that asset is modeled by a multi-dimentional jump diffusion with stochastic volatility. Otherwise, the first model considers the volatility as a continuous process and the second model considers it as a jump process. Finally in the 3rd model, the underlying asset is without jump and volatility follows a model CEV without jump. This model allow better to take into account some phenomena observed in the markets. We develop numerical methods that determine the values of prices for these options. We first write the model as an integro-differential stochastic equations system "EIDS," of which we study existence and unicity of solutions. Then we relate the resolution of PIDE to the computation of the option value.
Download or read book Option Pricing with Long Memory Stochastic Volatility Models written by Zhigang Tong and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is now known that long memory stochastic volatility models can capture the well-documented evidence of volatility persistence. However, due to the complex structures of the long memory processes, the analytical formulas for option prices are not available yet. In this book, we propose two fractional continuous time stochastic volatility models which are built on the popular short memory stochastic volatility models. Using the tools from stochastic calculus, fractional calculus and Fourier transform, we derive the (approximate) analytical solutions for option prices. We also numerically study the effects of long memory on option prices. We show that the fractional integration parameter has the opposite effect to that of volatility of volatility parameter. We also find that long memory models can accommodate the short term options and the decay of volatility skew better than the corresponding short memory models. These findings would appeal to the researchers and practitioners in the areas of quantitative finance.
Download or read book Credit Risk Frontiers written by Tomasz Bielecki and published by John Wiley & Sons. This book was released on 2011-02-08 with total page 770 pages. Available in PDF, EPUB and Kindle. Book excerpt: A timely guide to understanding and implementing credit derivatives Credit derivatives are here to stay and will continue to play a role in finance in the future. But what will that role be? What issues and challenges should be addressed? And what lessons can be learned from the credit mess? Credit Risk Frontiers offers answers to these and other questions by presenting the latest research in this field and addressing important issues exposed by the financial crisis. It covers this subject from a real world perspective, tackling issues such as liquidity, poor data, and credit spreads, as well as the latest innovations in portfolio products and hedging and risk management techniques. Provides a coherent presentation of recent advances in the theory and practice of credit derivatives Takes into account the new products and risk requirements of a post financial crisis world Contains information regarding various aspects of the credit derivative market as well as cutting edge research regarding those aspects If you want to gain a better understanding of how credit derivatives can help your trading or investing endeavors, then Credit Risk Frontiers is a book you need to read.
Download or read book Log Normal Stochastic Volatility Model written by Artur Sepp and published by . This book was released on 2016 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: While empirical studies have established that the log-normal stochastic volatility (SV) model is superior to its alternatives, the model does not allow for the analytical solutions available for affine models. To circumvent this, we show that the joint moment generating function (MGF) of the log-price and the quadratic variance (QV) under the log-normal SV model can be decomposed into a leading term, which is given by an exponential-affine form, and a residual term, whose estimate depends on the higher order moments of the volatility process. We prove that the second-order leading term is theoretically consistent with the expected values and covariance matrix of the log-price and the quadratic variance. We further extend this approach to the log-normal SV model with jumps. We use Fourier inversion techniques to value vanilla options on the equity and the QV and, by comparison to Monte Carlo simulations, we show that the second-order leading term is precise for the valuation of vanilla options. We generalize the affine decomposition to other non-affine stochastic volatility models with polynomial drift and volatility functions, and with jumps in the volatility process.
