Discrete Time Stochastic Volatility

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Discrete Time Stochastic Volatility Model

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Author : Guojing Tang
language : en
Publisher:
Release Date : 2009

Discrete Time Stochastic Volatility Model written by Guojing Tang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.

A New Class Of Discrete Time Stochastic Volatility Model With Correlated Errors

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Author : Sujay Mukhoti
language : en
Publisher:
Release Date : 2017

A New Class Of Discrete Time Stochastic Volatility Model With Correlated Errors written by Sujay Mukhoti and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.

In an efficient stock market, the returns and their time-dependent volatility are often jointly modeled by stochastic volatility models (SVMs). Over the last few decades several SVMs have been proposed to adequately capture the defining features of the relationship between the return and its volatility. Among one of the earliest SVM, Taylor (1982) proposed a hierarchical model, where the current return is a function of the current latent volatility, which is further modeled as an auto-regressive process. In an attempt to make the SVMs more appropriate for complex realistic market behavior, a leverage parameter was introduced in the Taylor's SVM, which however led to the violation of the efficient market hypothesis (EMH, a necessary mean-zero condition for the return distribution that prevents arbitrage possibilities). Subsequently, a host of alternative SVMs had been developed and are currently in use. In this paper, we propose mean-corrections for several generalizations of Taylor's SVM that capture the complex market behavior as well as satisfy EMH. We also establish a few theoretical results to characterize the key desirable features of these models, and present comparison with other popular competitors. Furthermore, four real-life examples (Oil price, CITI bank stock price, Euro-USD rate, and S&P 500 index returns) have been used to demonstrate the performance of this new class of SVMs.

Discrete Time Stochastic Volatility Models And Mcmc Based Statistical Inference

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Author : Nikolaus Hautsch
language : en
Publisher:
Release Date : 2008

Discrete Time Stochastic Volatility Models And Mcmc Based Statistical Inference written by Nikolaus Hautsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.

Discrete Time Stochastic Volatility

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Author : Thomas Roos
language : en
Publisher:
Release Date : 2017

Discrete Time Stochastic Volatility written by Thomas Roos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.

We propose a new methodology for obtaining arbitrage free European option prices from a SABR-like parameterisation. The method consists of specifying the joint distribution of the volatility and underlying at a given expiry and requires the calculation of a simple one-dimensional numerical integral per option price. CMS prices and some more general payouts can also be obtained as one-dimensional integrals. The specification of the volatility function is flexible and allows additional control over the wings of the distribution. The approach itself is general and applicable to a variety of asset classes.

Stochastic Volatility Long Term Option And Discrete Time Problems In Fx

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Author : Francois-Stephane Robert Mantion
language : en
Publisher:
Release Date : 1998

Stochastic Volatility Long Term Option And Discrete Time Problems In Fx written by Francois-Stephane Robert Mantion and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Vix Computation Based On Affine Stochastic Volatility Models In Discrete Time

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Author : Asmerilda Hitaj
language : en
Publisher:
Release Date : 2015

Vix Computation Based On Affine Stochastic Volatility Models In Discrete Time written by Asmerilda Hitaj and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with categories.

We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, captures the time-varying higher moments observed in financial series. We build this class of models in order to reach two desirable results. Firstly, we have a recursive procedure for the characteristic function of the log price at maturity that allows a semi-analytical formula for option prices as in Heston and Nandi (2000). Secondly, we try to reproduce some features of the VIX Index. We derive a simple formula for the VIX index and use it for option pricing purposes.

Double Gamma Stochastic Volatility Model In Discrete Time

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Author : Ali Hirsa
language : en
Publisher:
Release Date : 2017

Double Gamma Stochastic Volatility Model In Discrete Time written by Ali Hirsa and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.

In an affine term structure framework we propose a discrete time stochastic volatility model. We derive the characteristic function of the log swap rate under swap measure. Having the characteristic function, we employ the Fourier cosine (COS) technique to price swaptions. Using data on tweleve years of swap rates and swaption premiums, model parameters are estimated using an unscented Kalman filter algorithm.

Stochastic Volatility Option Pricing In Discrete Time

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Author : Victor K. Ng
language : en
Publisher:
Release Date : 1991

Stochastic Volatility Option Pricing In Discrete Time written by Victor K. Ng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Options (Finance) categories.

Stochastic Volatility Long Term Options And Discrete Time Problems In Fx

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Author : Francois-Stephane Robert Andre Mantion
language : en
Publisher:
Release Date : 1998

Stochastic Volatility Long Term Options And Discrete Time Problems In Fx written by Francois-Stephane Robert Andre Mantion and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.

Discrete Time Series Processes And Applications In Finance

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Author : Gilles Zumbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-04

Discrete Time Series Processes And Applications In Finance written by Gilles Zumbach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-04 with Mathematics categories.

Most financial and investment decisions are based on considerations of possible future changes and require forecasts on the evolution of the financial world. Time series and processes are the natural tools for describing the dynamic behavior of financial data, leading to the required forecasts. This book presents a survey of the empirical properties of financial time series, their descriptions by means of mathematical processes, and some implications for important financial applications used in many areas like risk evaluation, option pricing or portfolio construction. The statistical tools used to extract information from raw data are introduced. Extensive multiscale empirical statistics provide a solid benchmark of stylized facts (heteroskedasticity, long memory, fat-tails, leverage...), in order to assess various mathematical structures that can capture the observed regularities. The author introduces a broad range of processes and evaluates them systematically against the benchmark, summarizing the successes and limitations of these models from an empirical point of view. The outcome is that only multiscale ARCH processes with long memory, discrete multiplicative structures and non-normal innovations are able to capture correctly the empirical properties. In particular, only a discrete time series framework allows to capture all the stylized facts in a process, whereas the stochastic calculus used in the continuum limit is too constraining. The present volume offers various applications and extensions for this class of processes including high-frequency volatility estimators, market risk evaluation, covariance estimation and multivariate extensions of the processes. The book discusses many practical implications and is addressed to practitioners and quants in the financial industry, as well as to academics, including graduate (Master or PhD level) students. The prerequisites are basic statistics and some elementary financial mathematics.