Download or read book Empirical Analysis of Affine vs Non Affine Variance Specifications in Jump Diffusion Models for Equity Indices written by Katja Ignatieva and published by . This book was released on 2015 with total page 49 pages. Available in PDF, EPUB and Kindle. Book excerpt: How to model the variance process driving stock returns is a major research questions in finance. The specification of a variance model has implications for, e.g., risk management decisions, portfolio allocation or derivative pricing. This paper analyzes several crucial questions for setting up a variance model. (i) Are jumps an important model ingredient even when using a non-affine specification? (ii) How do affine specifications perform when compared to non-affine models. (iii) How should non-linearities be modeled? We find that, first, jump models clearly outperform pure stochastic volatility models. Second, non-affine specifications outperform affine models, even after including jumps. And finally, we find that the polynomial specification of the drift term, that has also been used in short rate models, is the best non-affine model under consideration.
Download or read book Estimation of Affine Jump Diffusions Using Realized Variance and Bipower Variation in Empirical Characteristic Function Method written by Alex Levin and published by . This book was released on 2015 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extensions of Empirical Characteristic Function (ECF) method for estimating parameters of affine jump-diffusions with unobserved stochastic volatility (SV) are considered. We develop a new approach based on a bias-corrected ECF for the Realized Variance (in the case of diffusions) and Bipower Variation or second generation jump-robust estimators of integrated stochastic variance (in the case of jumps in the underlying). Effective numerical implementation of Unconditional and Conditional ECF methods through a special configuration of grid points in the frequency domain is proposed. The method is illustrated based on a multifactor jump-diffusion SV model with exponential Poisson jumps in the volatility and underlying correlated by a new ''Gamma-factor copula'' that allows for analytically tractable joint characteristic function. A closed form Lauricella-Kummer-type density is derived for the stationary SV distribution. This distribution extends in a certain way a Generalized Gamma Convolution family of Thorin, and it is proven to be infinitely divisible, but not always self-decomposable. Numerical results for S&P 500 Index, VIX Index and rigorous Monte-Carlo study for a number of SV models are presented.
Download or read book Out of Sample Performance of Jump Diffusion Models for Equity Indices written by Roman Frey and published by . This book was released on 2015 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: Out-of-sample performance of continuous time models for equity returns is crucial in practical applications such as computing risk measures like value at risk, determine optimal portfolios or pricing derivatives. For all these applications investors need to model the return distribution of an underlying at some point in time in the future given current information. In this paper we analyze the out-of-sample performance of exponentially affine and non-affine continuous time stochastic volatility models with jumps in returns and volatility. Our analysis evaluates the density forecasts implied by the models. In a first step, we find in general that the good in-sample fits reported in the related literature do not carry over to the out-of-sample performance. In particular the left tail of the distribution poses a considerable challenge to the proposed models. In a second step, we analyze the models by using a rolling window approach. We find that using estimation periods that include high market stress events improve forecasting power considerably. In a third step, we apply parameters estimated on the sub period including the financial crisis (period with highest market stress) to all other forecasting sub periods. This approach further increases overall forecasting power and results in an outperformance of affine compared to non-affine models and an outperformance of jump models.
Download or read book Jump Activity Analysis for Affine Jump Diffusion Models written by José Da Fonseca and published by . This book was released on 2016 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this paper is to perform a joint analysis of jump activity for commodities and their respective volatility indices. Exploiting the property that for affine jump-diffusion models a volatility index, which is quoted on the market, is an affine function of the instantaneous volatility state variable (thus turning this quantity observable), we perform a test of common jumps for multidimensional processes to assess whether an asset and its volatility jump together. Applying this test to the crude oil pair USO/OVX and the gold pair GLD/GVZ we find strong evidence that for these two markets the asset and its volatility have disjoint jumps. This result contrasts with existing results for the equity market and underpins a very specific nature of the commodity market. The results are further confirmed by analysing jump size distributions using a copula methodology.
Download or read book Working Paper Series written by and published by . This book was released on 2001 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Jump diffusion Processes and Affine Term Structure Models written by J. Benson Durham and published by . This book was released on 2005 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt: Affine term structure models in which the short rate follows a jump-diffusion process are difficult to solve, and the parameters of such models are hard to estimate. Without analytical answers to the partial difference differential equation (PDDE) for bond prices implied by jump-diffusion processes, one must find a numerical solution to the PDDE or exactly solve an approximate PDDE. Although the literature focuses on a single linearization technique to estimate the PDDE, this paper outlines alternative methods that seem to improve accuracy. Also, closed-form solutions, numerical estimates, and closed-form approximations of the PDDE each ultimately depend on the presumed distribution of jump sizes, and this paper explores a broader set of possible densities that may be more consistent with intuition, including a bi-modal Gaussian mixture. GMM and MLE of one- and two-factor jump-diffusion models produce some evidence for jumps, but sensitivity analyses suggest sizeable confidence intervals around the parameters.
Download or read book Essays on Jump Diffusion Models in Asset Pricing and on the Prediction of Aggregate Stock Returns written by Roman Frey and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Diese Dissertation besteht aus drei individuellen Aufsätzen, die jeweils eine in sich geschlossene Forschungsarbeit darstellt. Im ersten Aufsatz, "Out-of-Sample Performance of Jump-Diffusion Models for Equity Indices: What the Financial Crisis was Good For", analysieren wir die out-of-sample Performance von zeitstetigen affinen und nicht affinen stochastischen Volatilitätsmodellen. Die out-of-sample Modellperformance ist eine Kennzahl mit zentraler Bedeutung für Investoren. Sie spielt unter anderem im Risikomanagement, der Asset Allocation wie auch in der Bewertung von derivativen Instrumenten, eine entscheidende Rolle. In dieser empirischen Studie, die auf täglichen Renditen des Aktienindex S&P 500 basiert, testen wir insgesamt 24 verschiedene Modellspezifikationen. Unser Testansatz evaluiert die durch die Modelle vorhergesagten Verteilungsdichten. Der entscheidende Vorteil dieser Methodik liegt darin, dass wir jeweils die gesamte modellinduzierte Dichte berücksichtigen. Unsere empirischen Resultate zeigen, dass sich die, in der Literatur häufig diskutierte, gute in-sample Modellperformance in out-of-sample Anwendungen generell nicht bestätigen lässt. Mittels eines rollierenden Zeitfensters beobachten wir, dass Modellparameter, die während einer genügend volatilen Marktphase geschätzt wurden, deutlich bessere out-of-sample Resultate liefern. Vielversprechend ist demzufolge die out-of-sample Performance, wenn die Modellparameter auf der sich kürzlich abgespielten Finanzkrise geschätzt und zur Vorhersage von Verteilungsdichten verwendet werden. Generell beobachten wir, dass zum einen affine Modelle bessere Resultate erreichen als nicht affine. Zum anderen deuten unsere Ergebnisse darauf hin, dass Modelle mit Sprüngen in den Renditen sowie Varianzen besser performen als pure Diffusionsmodelle. Der zweite Aufsatz mit dem Titel "Pricing CO2 Futures Options - Empirical In- and Out-of-Sample Performance Analysis" analys.
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 An Empirical Study of the Dynamics of Implied Volatility Indices written by Bujar Huskaj and published by . This book was released on 2015 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper compares the empirical performance of continuous time models for the dynamics of nine different implied volatility indices. The models include linear, quadratic and nonlinear drift specifications with affine, constant elasticity of variance (CEV) and stochastic elasticity of variance (SEV) diffusion parts. We find that a nonlinear drift specification is important when imposing an affine structure on the diffusion, whereas a simple linear drift is adequate with a CEV and SEV specification, of which the SEV is dominant. For all but two of the indices we investigate, the best specification is a SEV diffusion with linear drift. For gold and the USD/EUR exchange rate there is little difference between a CEV and SEV diffusion with linear drift.
Download or read book Essays on the Specification Testing for Dynamic Asset Pricing Models written by Jaeho Yun and published by . This book was released on 2009 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation consists of three essays on the subjects of specification testing on dynamic asset pricing models. In the first essay (with Yongmiao Hong), "A Simulation Test for Continuous-Time Models," we propose a simulation method to implement Hong and Li's (2005) transition density-based test for continuous-time models. The idea is to simulate a sequence of dynamic probability integral transforms, which is the key ingredient of Hong and Li's (2005) test. The proposed procedure is generally applicable whether or not the transition density of a continuous-time model has a closed form and is simple and computationally inexpensive. A Monte Carlo study shows that the proposed simulation test has very similar sizes and powers to the original Hong and Li's (2005) test. Furthermore, the performance of the simulation test is robust to the choice of the number of simulation iterations and the number of discretization steps between adjacent observations. In the second essay (with Yongmiao Hong), "A Specification Test for Stock Return Models," we propose a simulation-based specification testing method applicable to stochastic volatility models, based on Hong and Li (2005) and Johannes et al. (2008). We approximate a dynamic probability integral transform in Hong and Li' s (2005) density forecasting test, via the particle filters proposed by Johannes et al. (2008). With the proposed testing method, we conduct a comprehensive empirical study on some popular stock return models, such as the GARCH and stochastic volatility models, using the S&P 500 index returns. Our empirical analysis shows that all models are misspecified in terms of density forecast. Among models considered, however, the stochastic volatility models perform relatively well in both in- and out-of-sample. We also find that modeling the leverage effect provides a substantial improvement in the log stochastic volatility models. Our value-at-risk performance analysis results also support stochastic volatility models rather than GARCH models. In the third essay (with Yongmiao Hong), "Option Pricing and Density Forecast Performances of the Affine Jump Diffusion Models: the Role of Time-Varying Jump Risk Premia," we investigate out-of-sample option pricing and density forecast performances for the affine jump diffusion (AJD) models, using the S&P 500 stock index and the associated option contracts. In particular, we examine the role of time-varying jump risk premia in the AJD specifications. For comparison purposes, nonlinear asymmetric GARCH models are also considered. To evaluate density forecasting performances, we extend Hong and Li's (2005) specification testing method to be applicable to the famous AJD class of models, whether or not model-implied spot volatilities are available. For either case, we develop (i) the Fourier inversion of the closed-form conditional characteristic function and (ii) the Monte Carlo integration based on the particle filters proposed by Johannes et al. (2008). Our empirical analysis shows strong evidence in favor of time-varying jump risk premia in pricing cross-sectional options over time. However, for density forecasting performances, we could not find an AJD specification that successfully reconcile the dynamics implied by both time-series and options data.
Download or read book The Pricing and the Hedging of Equity Derivatives with Affine Jump Diffusion Models written by Paolo Verzella and published by . This book was released on 2006 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transform Analysis of Affine Jump Diffusion Processes with Applications to Asset Pricing written by Claude Rodrigue Bambe Moutsinga and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a class of models in asset pricing, whose underlying has dynamics of Affine jump diffusion type. We first present L evy processes with their properties. We then introduce Affine jump diffusion processes which are basically a particular class of L evy processes. Our motivation for these is driven by the fact that many financial models are built on them. Affine jump diffusion processes present good analytical properties that allow one to get close form formulas for a wide range of option pricing. The approach we use here is based on the paper by Duffie D, Pan J, and Singleton K. An example will show how incorporating parameters such as the volatility of the underlying asset in the model, can influence the resulting price of the financial instrument under consideration. We will also show how this class of models incorporate well known models, specially those used to model interest rates dynamics, like for instance the Vasicek model.
Download or read book Fast Calibration of the Affine and Quadratic Models written by Daniel Alexandre Bloch and published by . This book was released on 2016 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using the recent work of Alos and Ewald on option pricing approximations we extend their approach to some specific jump-diffusion models with stochastic interest rates, compute the Greeks and improve the accuracy of the approximations. Further, we obtain analytical solutions to the price of variance swap and volatility swap. Using these results we derive approximations to the equivalent implied volatility surface, and we relate the at-the-money forward term-structure of the surface when the correlation is set to zero to the volatility swap. To conclude we use in the FFT both a change of variable and the approximated call prices as control variates in the computation of more general jump-diffusion models, reducing the variance, making the call price square integrable and drastically increasing the speed of convergence.
Download or read book Index to Theses with Abstracts Accepted for Higher Degrees by the Universities of Great Britain and Ireland and the Council for National Academic Awards written by and published by . This book was released on 2007 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Saddlepoint Approximations for Affine Jump Diffusion Models written by Paul Glasserman and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Affine jump-diffusion (AJD) processes constitute a large and widely used class of continuous-time asset pricing models that balance tractability and flexibility in matching market data. The prices of e.g., bonds, options, and other assets in AJD models are given by extended pricing transforms that have an exponential-affine form; these transforms have been characterized in great generality by Duffie, Pan and Singleton [28]. Calculating model prices requires inversion of these transforms, and this has limited the application of AJD models to the comparatively small subclass for which the transforms are available in closed form. This article seeks to widen the scope of AJD models amenable to practical application through approximate transform inversion techniques. More specifically, we develop the use of saddlepoint approximations for AJD models. These approximations facilitate the calculation of prices in AJD models whose transforms are not available explicitly. We derive and test several alternative saddlepoint approximations and find that they produce accurate prices over a wide range of parameters.
Download or read book Jump diffusion Processes and Affine Term Structure Models written by Athanasios Orphanides and published by . This book was released on 2005 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Firms active in OTC derivative markets increasingly use margin agreements to reduce counterparty credit risk. Making several simplifying assumptions, I use both a quasi- analytic approach and a simulation approach to quantify how margining reduces counterparty credit exposure. Margining reduces counterparty credit exposure by over 80 percent, using baseline parameter assumptions. I show how expected positive exposure (EPE) depends on key terms of the margin agreement and the current mark-to-market value of the portfolio of contracts with the counterparty. I also discuss a possible shortcut that could be used by firms that can model EPE without margin but cannot achieve the higher level of sophistication needed to model EPE with margin"--Federal Reserve Board web site.
Download or read book Performance of Affine Jump Diffusion Models During The Financial Crisis written by and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
