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Download or read book Analysis of an Uncertain Volatility Model written by and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We examine, both from an analytical and numerical viewpoint, the uncertain volatility model by Hobson-Rogers in the framework of degenerate parabolic PDEs of Kolmogorov type.
Author : Robert Buff
Publisher : Springer Science & Business Media
ISBN 13 : 3642563236
Total Pages : 246 pages
Book Rating : 4.6/5 (425 download)
Download or read book Uncertain Volatility Models written by Robert Buff and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is one of the only books to describe uncertain volatility models in mathematical finance and their computer implementation for portfolios of vanilla, barrier and American options in equity and FX markets. Uncertain volatility models place subjective constraints on the volatility of the stochastic process of the underlying asset and evaluate option portfolios under worst- and best-case scenarios. This book, which is bundled with software, is aimed at graduate students, researchers and practitioners who wish to study advanced aspects of volatility risk in portfolios of vanilla and exotic options. The reader is assumed to be familiar with arbitrage pricing theory.
Author : Bin Ren
Publisher :
ISBN 13 : 9781303052712
Total Pages : 112 pages
Book Rating : 4.0/5 (527 download)
Download or read book Asymptotic Behavior of Worst Case Scenario Prices in Uncertain Volatility Models written by Bin Ren and published by . This book was released on 2013 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: We mainly study the asymptotic behavior of the worst case scenario option prices as the volatility interval in an uncertain volatility model (UVM) degenerates to a single point, and then provide an approximation procedure for the worst case scenario prices in a UVM with small volatility interval. Numerical experiments show that this approximation procedure performs well even as the size of the volatility band is not sosmall.
Author : Changhong He
Publisher :
ISBN 13 :
Total Pages : 312 pages
Book Rating : 4.E/5 ( download)
Download or read book Estimation of Volatilities Under a Merton's Jump-diffusion Model and an Uncertain Volatility Model written by Changhong He and published by . This book was released on 2005 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : George J Kaye
Publisher : World Scientific Publishing Company
ISBN 13 : 1908979585
Total Pages : 438 pages
Book Rating : 4.9/5 (89 download)
Download or read book Value Of Uncertainty, The: Dealing With Risk In The Equity Derivatives Market written by George J Kaye and published by World Scientific Publishing Company. This book was released on 2012-11-16 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with the extraordinary growth in the derivatives market over the last decade, the impact of model choice, and model parameter usage, has become a major source of valuation uncertainty. This book concentrates on equity derivatives and charts, step by step, how key assumptions on the dynamics of stocks impact on the value of exotics. The presentation is technical, but maintains a strong focus on intuition and practical application./a
Author : Lorenzo Bergomi
Publisher : CRC Press
ISBN 13 : 1482244071
Total Pages : 520 pages
Book Rating : 4.4/5 (822 download)
Download or read book Stochastic Volatility Modeling written by Lorenzo Bergomi and published by CRC Press. This book was released on 2015-12-16 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Packed with insights, Lorenzo Bergomi's Stochastic Volatility Modeling explains how stochastic volatility is used to address issues arising in the modeling of derivatives, including:Which trading issues do we tackle with stochastic volatility? How do we design models and assess their relevance? How do we tell which models are usable and when does c
Author : Asli Oztukel
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (93 download)
Download or read book Uncertain Parameters, an Empirical Stochastic Volatility Model and Confidence Limits written by Asli Oztukel and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jean-Pierre Fouque
Publisher : Cambridge University Press
ISBN 13 : 9780521791632
Total Pages : 222 pages
Book Rating : 4.7/5 (916 download)
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.
Author : Tony S. Wirjanto
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book Bayesian Analysis of a Threshold Stochastic Volatility Model written by Tony S. Wirjanto and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper proposes a parsimonious threshold stochastic volatility (SV) model for financial asset returns. Instead of imposing a threshold value on the dynamics of the latent volatility process of the SV model, we assume that the innovation of the mean equation follows a threshold distribution in which the mean innovation switches between two regimes. In our model, the threshold is treated as an unknown parameter. We show that the proposed threshold SV model not only can capture the time-varying volatility of returns, but also can accommodate the asymmetric shape of conditional distribution of the returns. Parameter estimation is carried out by using Markov Chain Monte Carlo methods. For model selection and volatility forecast, an auxiliary particle filter technique is employed to approximate the filter and prediction distributions of the returns. Several experiments are conducted to assess the robustness of the proposed model and estimation methods. In the empirical study, we apply our threshold SV model to three return time series. The empirical analysis results show that the threshold parameter has a nonzero value and the mean innovations belong to two separately distinct regimes. We also find that the model with an unknown threshold parameter value consistently outperforms the model with a known threshold parameter value.
Author : Hwagyun Kim
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (129 download)
Download or read book Macroeconomic Uncertainty and Asset Prices written by Hwagyun Kim and published by . This book was released on 2011 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we measure the time-varying uncertainty of macroeconomic fluctuations and study its link to asset returns via a consumption-based asset pricing model. To this end, we introduce a stochastic volatility model employing a latent nonstationary common volatility with two asymptotic regimes and smooth transition between them. We define the common volatility factor extracted from consumption and dividend growth rates as the macroeconomic uncertainty and analyze its effects on asset prices using a model with the Epstein-Zin-Weil preferences. The presence of smooth transition in our volatility model creates another layer of uncertainty in macroeconomic fluctuations, and thus provides an additional channel that generates a sizable risk premium for even a small amount of the consumption volatility. The channel can play an important role in determining asset prices, especially if the perceived macroeconomic uncertainty unravels slowly. Our estimates for the risk aversion and elasticity of intertemporal substitution are both around two, and the simulation results show that the model matches the first and the second moments of market return and the risk-free rate, hence the equity premium.
Author : Marco Avellaneda
Publisher : World Scientific
ISBN 13 : 9789810237899
Total Pages : 390 pages
Book Rating : 4.2/5 (378 download)
Download or read book Quantitative Analysis in Financial Markets written by Marco Avellaneda and published by World Scientific. This book was released on 1999 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures delivered at the Seminar in Mathematical Finance at the Courant Institute, New York University. Subjects covered include: the emerging science of pricing and hedging derivative securities, managing financial risk, and price forecasting using statistics.
Author : Damiano Brigo
Publisher : Springer Science & Business Media
ISBN 13 : 354034604X
Total Pages : 1016 pages
Book Rating : 4.5/5 (43 download)
Download or read book Interest Rate Models - Theory and Practice written by Damiano Brigo and published by Springer Science & Business Media. This book was released on 2007-09-26 with total page 1016 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2nd edition of this successful book has several new features. The calibration discussion of the basic LIBOR market model has been enriched considerably, with an analysis of the impact of the swaptions interpolation technique and of the exogenous instantaneous correlation on the calibration outputs. A discussion of historical estimation of the instantaneous correlation matrix and of rank reduction has been added, and a LIBOR-model consistent swaption-volatility interpolation technique has been introduced. The old sections devoted to the smile issue in the LIBOR market model have been enlarged into a new chapter. New sections on local-volatility dynamics, and on stochastic volatility models have been added, with a thorough treatment of the recently developed uncertain-volatility approach. Examples of calibrations to real market data are now considered. The fast-growing interest for hybrid products has led to a new chapter. A special focus here is devoted to the pricing of inflation-linked derivatives. The three final new chapters of this second edition are devoted to credit. Since Credit Derivatives are increasingly fundamental, and since in the reduced-form modeling framework much of the technique involved is analogous to interest-rate modeling, Credit Derivatives -- mostly Credit Default Swaps (CDS), CDS Options and Constant Maturity CDS - are discussed, building on the basic short rate-models and market models introduced earlier for the default-free market. Counterparty risk in interest rate payoff valuation is also considered, motivated by the recent Basel II framework developments.
Author : Hua Lv
Publisher :
ISBN 13 : 9781267416353
Total Pages : 172 pages
Book Rating : 4.4/5 (163 download)
Download or read book Modeling, Calibration and Simulation of Spot Price Paths written by Hua Lv and published by . This book was released on 2012 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: We introduce some popular models in the energy markets. Then we propose to incorporate a stochastic volatility feature to an existing multi-factor deterministic volatility model in order to take into account the observed implied volatility skews for each of the commodities in the simulation of monthly forward prices. As examples we consider natural gas, crude oil and heating oil price and option data. Our objective is to explore the role of stochastic volatility modeling for calibration and simulation of price paths and scenario analysis. The linkage between price, option data and modeling is captured by the so called "Vs" in our approach. These are the effective group market parameters that capture the main impact of an uncertain and fluctuating volatility, in particular how these affect prices. To explore the significance of incorporating this link we carry out an initial calibration test to explore the role of the "Vs" in the commodity price distribution. We find that indeed the distribution of the commodity prices are significantly affected by incorporating the leading correction that accounts for the effect of uncertain volatility parameters which manifests itself in the data via strong "skew" effect in the option pricing data. An added benefit of this modeling framework is that it enables us to use observations around and not only at the money in a consistent way, thus, providing robustness and stability in calibration also at the order one level.
Author : N. V. Krylov
Publisher : Springer Science & Business Media
ISBN 13 : 3540709142
Total Pages : 314 pages
Book Rating : 4.5/5 (47 download)
Download or read book Controlled Diffusion Processes written by N. V. Krylov and published by Springer Science & Business Media. This book was released on 2008-09-26 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. ~urin~ that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in Wonham [76]). At the same time, Girsanov [25] and Howard [26] made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier [4]. Two types of engineering problems engendered two different parts of stochastic control theory. Problems of the first type are associated with multistep decision making in discrete time, and are treated in the theory of discrete stochastic dynamic programming. For more on this theory, we note in addition to the work of Howard and Bellman, mentioned above, the books by Derman [8], Mine and Osaki [55], and Dynkin and Yushkevich [12]. Another class of engineering problems which encouraged the development of the theory of stochastic control involves time continuous control of a dynamic system in the presence of random noise. The case where the system is described by a differential equation and the noise is modeled as a time continuous random process is the core of the optimal control theory of diffusion processes. This book deals with this latter theory.
Author : Eric Jacquier
Publisher :
ISBN 13 :
Total Pages : 31 pages
Book Rating : 4.:/5 (129 download)
Download or read book Bayesian Analysis of a Stochastic Volatility Model with Leverage Effect and Fat Tails written by Eric Jacquier and published by . This book was released on 2001 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic univariate stochastic volatility model specifies that conditional volatility follows a log-normal auto-regressive model with innovations assumed to be independent of the innovations in the conditional mean equation. Since the introduction of practical methods for inference in the basic volatility model (JPR-(1994)), it has been observed that the basic model is too restrictive for many financial series. We extend the basic SVOL to allow for a so-called quot;Leverage effectquot; via correlation between the volatility and mean innovations, and for fat-tails in the mean equation innovation. A Bayesian Markov Chain Monte Carlo algorithm is developed for the extended volatility model. Thus far, likelihood-based inference for the correlated SVOL model has not appeared in the literature. We develop Bayes Factors to assess the importance of the leverage and fat-tail extensions. Sampling experiments reveal little loss in precision from adding the model extensions but a large loss from using the basic model in the presence of mis-specification. For both equity and exchange rate data, there is overwhelming evidence in favor of models with fat-tailed volatility innovations, and for a leverage effect in the case of equity indices. We also find that volatility estimates from the extended model are markedly different from those produced by the basic SVOL.
Author : Samuel N. Cohen
Publisher : Springer Nature
ISBN 13 : 3030222853
Total Pages : 300 pages
Book Rating : 4.0/5 (32 download)
Download or read book Frontiers in Stochastic Analysis–BSDEs, SPDEs and their Applications written by Samuel N. Cohen and published by Springer Nature. This book was released on 2019-08-31 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of selected, revised and extended contributions resulted from a Workshop on BSDEs, SPDEs and their Applications that took place in Edinburgh, Scotland, July 2017 and included the 8th World Symposium on BSDEs. The volume addresses recent advances involving backward stochastic differential equations (BSDEs) and stochastic partial differential equations (SPDEs). These equations are of fundamental importance in modelling of biological, physical and economic systems, and underpin many problems in control of random systems, mathematical finance, stochastic filtering and data assimilation. The papers in this volume seek to understand these equations, and to use them to build our understanding in other areas of mathematics. This volume will be of interest to those working at the forefront of modern probability theory, both established researchers and graduate students.
Author : Marco Avellaneda
Publisher : World Scientific
ISBN 13 : 9789810246938
Total Pages : 372 pages
Book Rating : 4.2/5 (469 download)
Download or read book Quantitative Analysis in Financial Markets written by Marco Avellaneda and published by World Scientific. This book was released on 1999 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains lectures presented at the Courant Institute's Mathematical Finance Seminar.
