Download or read book Stochastic Volatility Double Jump Diffusions Model written by Youfa Sun and published by . This book was released on 2015 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research examines if there exists an appealing distribution for jump amplitude in the sense that with this distribution, the stochastic volatility double jump-diffusions (SVJJ) model would potentially have a superior option market fit while keeping a sound balance between reality and tractability. We provide a general methodology for pricing vanilla options via Fourier cosine series expansion method, in the setting of Heston's SVJJ (HSVJJ) model that may allow a range of jump amplitude distributions. Example applications include the normal (N) distribution, the exponential (E) distribution and the asymmetric double exponential (Db-E) distribution, regarding to analytical tractability for options and economical interpretation. An illustrative example examines the implications of HSVJJ model in capturing option 'smirks'. This example highlights the impacts on implied volatility surface of various jump amplitude distributions, through both extensive model calibrations and carefully designed implied-volatility impacting experiments. Numerical results show that, with the Db-E jump distribution, the HSVJJ model not only captures the implied volatility smile and smirk, but also the 'sadness'

Download or read book Double jump Diffusion Model for VIX written by Xin Zang and published by . This book was released on 2016 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper studies the continuous-time dynamics of VIX with stochastic volatility and jumps in VIX and volatility. Built on the general parametric affine model with stochastic volatility and jumps in the logarithm of VIX, we derive a linear relationship between the stochastic volatility factor and the VVIX index. We detect the existence of a co-jump of VIX and VVIX and put forward a double-jump stochastic volatility model for VIX through its joint property with VVIX. Using the VVIX index as a proxy for stochastic volatility, we use the MCMC method to estimate the dynamics of VIX. Comparing nested models of VIX, we show that the jump in VIX and the volatility factor are statistically significant. The jump intensity is also stochastic. We analyze the impact of the jump factor on VIX dynamics.

Download or read book A Jump diffusion Model with Stochastic Volatility and Durations written by Wei Wei and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Jump Diffusion and Stochastic Volatility Models in Securities Pricing written by Mthuli Ncube and published by . This book was released on 2012 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quantitative Finance written by Maria C. Mariani and published by John Wiley & Sons. This book was released on 2019-11-06 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a multitude of topics relevant to the quantitative finance community by combining the best of the theory with the usefulness of applications Written by accomplished teachers and researchers in the field, this book presents quantitative finance theory through applications to specific practical problems and comes with accompanying coding techniques in R and MATLAB, and some generic pseudo-algorithms to modern finance. It also offers over 300 examples and exercises that are appropriate for the beginning student as well as the practitioner in the field. The Quantitative Finance book is divided into four parts. Part One begins by providing readers with the theoretical backdrop needed from probability and stochastic processes. We also present some useful finance concepts used throughout the book. In part two of the book we present the classical Black-Scholes-Merton model in a uniquely accessible and understandable way. Implied volatility as well as local volatility surfaces are also discussed. Next, solutions to Partial Differential Equations (PDE), wavelets and Fourier transforms are presented. Several methodologies for pricing options namely, tree methods, finite difference method and Monte Carlo simulation methods are also discussed. We conclude this part with a discussion on stochastic differential equations (SDE’s). In the third part of this book, several new and advanced models from current literature such as general Lvy processes, nonlinear PDE's for stochastic volatility models in a transaction fee market, PDE's in a jump-diffusion with stochastic volatility models and factor and copulas models are discussed. In part four of the book, we conclude with a solid presentation of the typical topics in fixed income securities and derivatives. We discuss models for pricing bonds market, marketable securities, credit default swaps (CDS) and securitizations. Classroom-tested over a three-year period with the input of students and experienced practitioners Emphasizes the volatility of financial analyses and interpretations Weaves theory with application throughout the book Utilizes R and MATLAB software programs Presents pseudo-algorithms for readers who do not have access to any particular programming system Supplemented with extensive author-maintained web site that includes helpful teaching hints, data sets, software programs, and additional content Quantitative Finance is an ideal textbook for upper-undergraduate and beginning graduate students in statistics, financial engineering, quantitative finance, and mathematical finance programs. It will also appeal to practitioners in the same fields.

Download or read book An Examination on the Roles of Diffusions and Stochastic Volatility in the Exponential Levy Jumps Models written by Elton Daal and published by . This book was released on 2006 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent studies have shown that stochastic volatility in a continuous-time framework provides an excellent fit for financial asset returns when combined with finite-activity Merton's type compound Poisson Jump-diffusion models. However, we demonstrate that stochastic volatility does not play a central role when incorporated with infinite-activity Leacute;vy type pure jump models such as variance-gamma and normal inverse Gaussian processes to model high and low frequency historical time-series SP500 index returns. In addition, whether sources of stochastic volatility are diffusions or jumps are not relevant to improve the overall empirical fits of returns. Nevertheless, stochastic diffusion volatility with infinite-activity Levy jumps processes considerably reduces SP500 index call option in-sample and out-of-sample pricing errors of long-term ATM and OTM options, which contributed to a substantial improvement of pricing performances of SVJ and EVGSV models, compared to constant volatility Levy-type pure jumps models and/or stochastic volatility model without jumps. Interestingly, unlike asset returns, whether pure Levy jumps specifications are finite or infinite activity is not an important factor to enhance option pricing model performances once stochastic volatility is incorporated. Option prices are computed via improved Fast Fourier Transform algorithm using characteristic functions to match arbitrary log-strike grids with equal intervals with each moneyness and maturity of actual market option prices considered in this paper.

Download or read book A New Class of Stochastic Volatility Models with Jumps written by Mikhail Chernov and published by . This book was released on 2012 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this paper is to propose a new class of jump diffusions which feature both stochastic volatility and random intensity jumps. Previous studies have focused primarily on pure jump processes with constant intensity and log-normal jumps or constant jump intensity combined with a one factor stochastic volatility model. We introduce several generalizations which can better accommodate several empirical features of returns data. In their most general form we introduce a class of processes which nests jump-diffusions previously considered in empirical work and includes the affine class of random intensity models studied by Bates (1998) and Duffie, Pan and Singleton (1998) but also allows for non-affine random intensity jump components. We attain the generality of our specification through a generic Levy process characterization of the jump component. The processes we introduce share the desirable feature with the affine class that they yield analytically tractable and explicit option pricing formula. The non-affine class of processes we study include specifications where the random intensity jump component depends on the size of the previous jump which represent an alternative to affine random intensity jump processes which feature correlation between the stochastic volatility and jump component. We also allow for and experiment with different empirical specifications of the jump size distributions. We use two types of data sets. One involves the Samp;P500 and the other comprises of 100 years of daily Dow Jones index. The former is a return series often used in the literature and allows us to compare our results with previous studies. The latter has the advantage to provide a long time series and enhances the possibility of estimating the jump component more precisely. The non-affine random intensity jump processes are more parsimonious than the affine class and appear to fit the data much better.

Download or read book Calibration and Pricing Under a Stochastic Volatility Jump Diffusion Model with Time dependent Parameters written by and published by . This book was released on 2010 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book An Empirical Testing of a Jump diffusion Pricing Model with Stochastic Volatility written by Thomas More Arnold and published by . This book was released on 1998 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Does Observed Skewness and Kurtosis Imply a Stochastic Volatility Or Jump Diffusion Model written by Thomas J. Mather and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hedging Exotic Options in Stochastic Volatility and Jump Diffusion Models written by Kai Detlefsen and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Hull and White Formula for a General Stochastic Volatility Jump diffusion Model with Applications to the Study of the Short time Behavior of the Implied Volatility written by Elisa Alós and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Financial Modelling with Jump Processes written by Peter Tankov and published by CRC Press. This book was released on 2003-12-30 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematic

Download or read book Implied Calibration and Moments Asymptotics in Stochastic Volatility Jump Diffusion Models written by Stefano Galluccio and published by . This book was released on 2008 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the context of arbitrage-free modelling of financial derivatives, we introduce a novel calibration technique for models in the affine-quadratic class for the purpose of over-the-counter option pricing and risk-management. In particular, we aim at calibrating a stochastic volatility jump diffusion model to the whole market implied volatility surface at any given time. We study the asymptotic behaviour of the moments of the underlying distribution and use this information to introduce and implement our calibration algorithm. We numerically show that the proposed approach is both statistically stable and accurate.

Download or read book Optimal Portfolio Problem for Stochastic Volatility Jump Diffusion Models with Jump Bankruptcy Condition written by Floyd B. Hanson and published by . This book was released on 2008 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper treats the risk-averse optimal portfolio problem with consumption in continuous time with a stochastic-volatility, jump-diffusion (SVJD) model of the underlying risky asset and the volatility. The new developments are the use of the SVJD model with double-uniform jump-amplitude distributions and time-varying market parameters for the optimal portfolio problem. Although unlimited borrowing and short-selling play an important role in pure diffusion models, it is shown that borrowing and short selling are constrained for jump-diffusions. Finite range jump-amplitude models can allow constraints to be very large in contrast to infinite range models which severely restrict the optimal instantaneous stock-fraction to [0,1]. The reasonable constraints in the optimal stock-fraction due to jumps in the wealth argument for stochastic dynamic programming jump integrals remove a singularity in the stock-fraction due to vanishing volatility. Main modifications for the usual constant relative risk aversion (CRRA) power utility model are for handling the partial integro-differential equation (PIDE) resulting from the additional variance independent variable, instead of the ordinary integro-differential equation (OIDE) found for the pure jump-diffusion model of the wealth process. In addition to natural constraints due to jumps when enforcing the positivity of wealth condition, other constraints are considered for all practical purposes under finite market conditions. Also, a computationally practical solution of Heston's (1993) square-root-diffusion model for the underlying asset variance is derived. This shows that the non-negativity of the variance is preserved through the proper singular limit of a simple perfect-square form. An exact, non -singular solution is found for a special combination of the Heston stochastic volatility parameters.

Download or read book Applied Stochastic Processes and Control for Jump Diffusions written by Floyd B. Hanson and published by SIAM. This book was released on 2007-01-01 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump diffusions in continuous time. The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems.

Download or read book Hedging Analysis of Exotic Derivates in Stochastic Volatility and Jump Diffusion Models written by Peter Merrath and published by . This book was released on 2007 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: