A New Class Of Stochastic Volatility Models With Jumps
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A New Class Of Stochastic Volatility Models With Jumps Theory And Estimation
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Author : CIRANO.
language : en
Publisher: Montréal : CIRANO
Release Date : 1999
A New Class Of Stochastic Volatility Models With Jumps Theory And Estimation written by CIRANO. and has been published by Montréal : CIRANO this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
A New Class Of Stochastic Volatility Models With Jumps
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Author : Mikhail Chernov
language : en
Publisher:
Release Date : 2012
A New Class Of Stochastic Volatility Models With Jumps written by Mikhail Chernov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
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.
Inference For A Class Of Stochastic Volatility Models In Presence Of Jumps
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Author : Petra Posedel
language : en
Publisher:
Release Date : 2007
Inference For A Class Of Stochastic Volatility Models In Presence Of Jumps written by Petra Posedel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
Jump Diffusion And Stochastic Volatility Models In Securities Pricing
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Author : Mthuli Ncube
language : en
Publisher:
Release Date : 2012
Jump Diffusion And Stochastic Volatility Models In Securities Pricing written by Mthuli Ncube and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with categories.
From Martingale Schrodinger Bridges To A New Class Of Stochastic Volatility Model
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Author : Pierre Henry-Labordere
language : en
Publisher:
Release Date : 2019
From Martingale Schrodinger Bridges To A New Class Of Stochastic Volatility Model written by Pierre Henry-Labordere and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Following closely the construction of the Schrodinger bridge, we build a new class of Stochastic Volatility Models exactly calibrated to market instruments such as for example Vanillas and options on realized variance. These models differ strongly from the well-known local stochastic volatility models, in particular the instantaneous volatility-of-volatility of the associated naked SVMs is not modified, once calibrated to market instruments. They can be interpreted as a martingale version of the Schrodinger bridge. The numerical calibration is performed using a dynamic-like version of the Sinkhorn algorithm. We finally highlight a striking relation with Dyson non-colliding Brownian motions.
Stochastic Volatility And Jumps
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Author : Katja Ignatieva
language : en
Publisher:
Release Date : 2009
Stochastic Volatility And Jumps written by Katja Ignatieva 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.
This paper analyzes exponentially affine and non-affine stochastic volatility models with jumps in returns and volatility. Markov Chain Monte Carlo (MCMC) technique is applied within a Bayesian inference to estimate model parameters and latent variables using daily returns from the Samp;P 500 stock index. There are two approaches to overcome the problem of misspecification of the square root stochastic volatility model. The first approach proposed by Christo ersen, Jacobs and Mimouni (2008) suggests to investigate some non-affine alternatives of the volatility process. The second approach consists in examining more heavily parametrized models by adding jumps to the return and possibly to the volatility process. The aim of this paper is to combine both model frameworks and to test whether the class of affine models is outperformed by the class of non-affine models if we include jumps into the stochastic processes. We conclude that the non-affine model structure have promising statistical properties and are worth further investigations. Further, we find affine models with jump components that perform similar to the non affine models without jump components. Since non affine models yield economically unrealistic parameter estimates, and research is rather developed for the affine model structures we have a tendency to prefer the affine jump diffusion models.
Modelling Stochastic Volatility With Leverage And Jumps
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Author : Sheheryar Malik
language : en
Publisher:
Release Date : 2010
Modelling Stochastic Volatility With Leverage And Jumps written by Sheheryar Malik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with categories.
In this paper we provide a unified methodology for conducting likelihood-based inference on the unknown parameters of a general class of discrete-time stochastic volatility (SV) models, characterized by both a leverage effect and jumps in returns. Given the nonlinear/non-Gaussian state-space form, approximating the likelihood for the parameters is conducted with output generated by the particle filter. Methods are employed to ensure that the approximating likelihood is continuous as a function of the unknown parameters thus enabling the use of standard Newton-Raphson type maximization algorithms. Our approach is robust and efficient relative to alternative Markov Chain Monte Carlo schemes employed in such contexts. In addition it provides a feasible basis for undertaking the nontrivial task of model comparison. Furthermore, we introduce new volatility model, namely SV-GARCH which attempts to bridge the gap between GARCH and stochastic volatility specifications. In nesting the standard GARCH model as a special case, it has the attractive feature of inheriting the same unconditional properties of the standard GARCH model but being conditionally heavier-tailed; thus more robust to outliers. It is demonstrated how this model can be estimated using the described methodology. The technique is applied to daily returns data for S&P 500 stock price index for various spans. In assessing the relative performance of SV with leverage and jumps and nested specifications, we find strong evidence in favour of a including leverage effect and jumps when modelling stochastic volatility. Additionally, we find very encouraging results for SV-GARCH in terms of predictive ability which is comparable to the other models considered.
A General Framework For Discretely Sampled Realized Variance Derivatives In Stochastic Volatility Models With Jumps
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Author : Zhenyu Cui
language : en
Publisher:
Release Date : 2018
A General Framework For Discretely Sampled Realized Variance Derivatives In Stochastic Volatility Models With Jumps written by Zhenyu Cui and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with categories.
After the recent financial crisis, the market for volatility derivatives has expanded rapidly to meet the demand from investors, risk managers and speculators seeking diversification of the volatility risk. In this paper, we develop a novel and efficient transform-based method to price swaps and options related to discretely-sampled realized variance under a general class of stochastic volatility models with jumps. We utilize frame duality and density projection method combined with a novel continuous-time Markov chain (CTMC) weak approximation scheme of the underlying variance process. Contracts considered include discrete variance swaps, discrete variance options, and discrete volatility options. Models considered include several popular stochastic volatility models with a general jump size distribution: Heston, Scott, Hull-White, Stein-Stein, alpha-Hypergeometric, 3/2 and 4/2 models. Our framework encompasses and extends the current literature on discretely sampled volatility derivatives, and provides highly efficient and accurate valuation methods. Numerical experiments confirm our findings.
A Class Of Stochastic Volatility Models For The Term Structure Of Interest Rates
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Author : Elisa Nicolato
language : en
Publisher:
Release Date : 1999
A Class Of Stochastic Volatility Models For The Term Structure Of Interest Rates written by Elisa Nicolato and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 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.