Download or read book A General decomposition formula for derivative prices in stochastic volatility models written by Elisa Alòs and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Derivatives in Financial Markets with Stochastic Volatility written by Jean-Pierre Fouque and published by Cambridge University Press. This book was released on 2000-07-03 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2000, addresses pricing and hedging derivative securities in uncertain and changing market volatility.
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 Pricing Derivatives in Stochastic Volatility Models Using the Finite Difference Method written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The Heston stochastic volatility model is one extension of the Black-Scholes model which describes the money markets more accurately so that more realistic prices for derivative products are obtained. From the stochastic differential equation of the underlying financial product a partial differential equation (p.d.e.) for the value function of an option can be derived. This p.d.e. can be solved with the finite difference method (f.d.m.). The stability and consistency of the method is examined. Furthermore a boundary condition is proposed to reduce the numerical error. Finally a non uniform structured grid is derived which is fairly optimal for the numerical result in the most interesting point.
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 A General Stochastic Volatility Model for the Pricing and Forecasting of Interest Rate Derivatives written by Anders B. Trolle and published by . This book was released on 2006 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features correlations between innovations to forward rates and volatilities, quasi-analytical prices of zero-coupon bond options and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finite-dimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities. The model also performs well in forecasting interest rates and derivatives.
Download or read book Modelling and Simulation of Stochastic Volatility in Finance written by Christian Kahl and published by Universal-Publishers. This book was released on 2008 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The famous Black-Scholes model was the starting point of a new financial industry and has been a very important pillar of all options trading since. One of its core assumptions is that the volatility of the underlying asset is constant. It was realised early that one has to specify a dynamic on the volatility itself to get closer to market behaviour. There are mainly two aspects making this fact apparent. Considering historical evolution of volatility by analysing time series data one observes erratic behaviour over time. Secondly, backing out implied volatility from daily traded plain vanilla options, the volatility changes with strike. The most common realisations of this phenomenon are the implied volatility smile or skew. The natural question arises how to extend the Black-Scholes model appropriately. Within this book the concept of stochastic volatility is analysed and discussed with special regard to the numerical problems occurring either in calibrating the model to the market implied volatility surface or in the numerical simulation of the two-dimensional system of stochastic differential equations required to price non-vanilla financial derivatives. We introduce a new stochastic volatility model, the so-called Hyp-Hyp model, and use Watanabe's calculus to find an analytical approximation to the model implied volatility. Further, the class of affine diffusion models, such as Heston, is analysed in view of using the characteristic function and Fourier inversion techniques to value European derivatives.
Download or read book Volatility written by Robert A. Jarrow and published by . This book was released on 1998 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a number of authors, this text is aimed at market practitioners and applies the latest stochastic volatility research findings to the analysis of stock prices. It includes commentary and analysis based on real-life situations.
Download or read book A General Stochastic Volatility Model for the Pricing of Interest Rate Derivatives written by Anders B. Trolle and published by . This book was released on 2016 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt: We develop a tractable and flexible stochastic volatility multi-factor model of the term structure of interest rates. It features unspanned stochastic volatility factors, correlation between innovations to forward rates and their volatilities, quasi-analytical prices of zero-coupon bond options, and dynamics of the forward rate curve, under both the actual and risk-neutral measure, in terms of a finitedimensional affine state vector. The model has a very good fit to an extensive panel data set of interest rates, swaptions and caps. In particular, the model matches the implied cap skews and the dynamics of implied volatilities.
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 Stochastic Volatility Models with Applications to Option Pricing written by K. Khorasani and published by . This book was released on 1998 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Extended Abstracts Summer 2015 written by Josep Díaz and published by Birkhäuser. This book was released on 2017-02-24 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is divided into two parts, the first of which seeks to connect the phase transitions of various disciplines, including game theory, and to explore the synergies between statistical physics and combinatorics. Phase Transitions has been an active multidisciplinary field of research, bringing together physicists, computer scientists and mathematicians. The main research theme explores how atomic agents that act locally and microscopically lead to discontinuous macroscopic changes. Adopting this perspective has proven to be especially useful in studying the evolution of random and usually complex or large combinatorial objects (like networks or logic formulas) with respect to discontinuous changes in global parameters like connectivity, satisfiability etc. There is, of course, an obvious strategic element in the formation of a transition: the atomic agents “selfishly” seek to optimize a local parameter. However, up to now this game-theoretic aspect of abrupt, locally triggered changes had not been extensively studied. In turn, the book’s second part is devoted to mathematical and computational methods applied to the pricing of financial contracts and the measurement of financial risks. The tools and techniques used to tackle these problems cover a wide spectrum of fields, like stochastic calculus, numerical analysis, partial differential equations, statistics and econometrics. Quantitative Finance is a highly active field of research and is increasingly attracting the interest of academics and practitioners alike. The material presented addresses a wide variety of new challenges for this audience.
Download or read book Analytical Solvability and Exact Simulation of Stochastic Volatility Models with Jumps written by Pingping Jiang and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We perform a thorough investigation on the analytical solvability of general stochastic volatility (SV) models with Levy jumps and propose a unified, accurate, and efficient almost exact simulation method to price various financial derivatives. Our theoretical results lay a foundation for a range of valuation, calibration, and econometric problems. Our almost exact simulation method is applicable to a broad class of models and enables effective pricing of path-dependent financial derivatives, whereas the traditional exact simulation method is always tailor-made for some specific models and is generally time-consuming, which limits its use in the case of path-dependent financial derivatives. More specifically, by combining a decomposition technique with a change of measure approach, we first develop a simple probabilistic method to derive a unified formula for the conditional characteristic function of the log-asset price under general SV models with Levy jumps and show under which conditions this new formula admits a closed-form expression. The conditional and unconditional joint characteristic functions of the log-asset price and the integrated variance can be easily obtained as byproducts. Second, we take advantage of our main theoretical result, the Hilbert transform method, the interpolation technique, and the dimension reduction technique to construct unified and efficient almost exact simulation schemes. Finally, we apply our almost exact simulation method to price European options, discretely monitored weighted variance swaps, and discretely monitored variance options under a wide variety of SV models with Levy jumps. Extensive numerical examples demonstrate the high level of accuracy and efficiency of our almost exact simulation method in terms of bias, root-mean-squared error (RMS error), and CPU time.
Download or read book Long memory Stochastic Volatility Models written by Libo Xie and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Volatility Models written by Jian Yang and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Volatility Models with Jumps and High Frequency Data written by Jonas Kau and published by . This book was released on 2009 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Stochastic Volatility Model with Realized Measures for Option Pricing written by Giacomo Bormetti and published by . This book was released on 2019 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both observed returns and realized measures to the latent conditional variance. A semi-analytical option pricing framework is developed for this class of models. In addition, we provide analytical filtering and smoothing recursions for the basic specification of the model, and an effective MCMC algorithm for its richer variants. The empirical analysis shows the effectiveness of filtering and smoothing realized measures in inflating the latent volatility persistence - the crucial parameter in pricing Standard and Poor's 500 Index options.
