The Estimation Of Stochastic Models In Finance With Volatility And Jump Intensity
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The Estimation Of Stochastic Models In Finance With Volatility And Jump Intensity
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Author : David Edward A. Wilson
language : en
Publisher:
Release Date : 2018
The Estimation Of Stochastic Models In Finance With Volatility And Jump Intensity written by David Edward A. Wilson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Finance categories.
This thesis covers the parametric estimation of models with stochastic volatility, jumps, and stochastic jump intensity, by FFT. The first primary contribution is a parametric minimum relative entropy optimal Q-measure for affine stochastic volatility jump-diffusion (ASVJD). Other attempts in the literature have minimized the relative entropy of Q given P either by nonparametric methods, or by numerical PDEs. These methods are often difficult to implement. We construct the relative entropy of Q given P from the Lebesgue densities under P and Q, respectively, where these can be retrieved by FFT from the closed form log-price characteristic function of any ASVJD model. We proceed by first estimating the fixed parameters of the P-measure by the Approximate Maximum Likelihood (AML) method of Bates (2006), and prove that the integrability conditions required for Fourier inversion are satisfied. Then by using a structure preserving parametric model under the Q-measure, we minimize the relative entropy of Q given P with respect to the model parameters under Q. AML can be used to estimate P within the ASVJD class. Since, AML is much faster than MCMC, our main supporting contributions are to the theory of AML. The second main contribution of this thesis is a non-affine model for time changed jumps with stochastic jump intensity called the Leveraged Jump Intensity (LJI) model. The jump intensity in the LJI model is modeled by the CIR process. Leverage occurs in the LJI model, since the Brownian motion driving the CIR process also appears in the log-price with a negative coefficient. Models with a leverage effect of this type are usually affine, but model the intensity with an Ornstein-Uhlenbeck process. The conditional characteristic function of the LJI log-price given the intensity is known in closed form. Thus, we price LJI call options by conditional Monte Carlo, using the Carr and Madan (1999) FFT formula for conditional pricing.
Essays On Stochastic Volatility And Jumps
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Author : Ke Chen (Economist)
language : en
Publisher:
Release Date : 2013
Essays On Stochastic Volatility And Jumps written by Ke Chen (Economist) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
This thesis studies a few different finance topics on the application and modelling of jump and stochastic volatility process. First, the thesis proposed a non-parametric method to estimate the impact of jump dependence, which is important for portfolio selection problem. Comparing with existing literature, the new approach requires much less restricted assumption on the jump process, and estimation results suggest that the economical significance of jumps is largely mis-estimated in portfolio optimization problem. Second, this thesis investigates the time varying variance risk premium, in a framework of stochastic volatility with stochastic jump intensity. The proposed model considers jump intensity as an extra factor which is driven by realized jumps, in addition to a stochastic volatility model. The results provide strong evidence of multiple factors in the market and show how they drive the variance risk premium. Thirdly, the thesis uses the proposed models to price options on equity and VIX consistently. Based on calibrated model parameters, the thesis shows how to calculate the unconditional correlation of VIX future between different maturities.
Financial Modelling With Jump Processes
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Author : Peter Tankov
language : en
Publisher: CRC Press
Release Date : 2003-12-30
Financial Modelling With Jump Processes written by Peter Tankov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-30 with Business & Economics categories.
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
Parameter Estimation In Stochastic Volatility Models
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Author : Jaya P. N. Bishwal
language : en
Publisher: Springer Nature
Release Date : 2022-08-06
Parameter Estimation In Stochastic Volatility Models written by Jaya P. N. Bishwal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-06 with Mathematics categories.
This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
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.
Stochastic Volatility And Realized Stochastic Volatility Models
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Author : Makoto Takahashi
language : en
Publisher: Springer Nature
Release Date : 2023-04-18
Stochastic Volatility And Realized Stochastic Volatility Models written by Makoto Takahashi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-18 with Business & Economics categories.
This treatise delves into the latest advancements in stochastic volatility models, highlighting the utilization of Markov chain Monte Carlo simulations for estimating model parameters and forecasting the volatility and quantiles of financial asset returns. The modeling of financial time series volatility constitutes a crucial aspect of finance, as it plays a vital role in predicting return distributions and managing risks. Among the various econometric models available, the stochastic volatility model has been a popular choice, particularly in comparison to other models, such as GARCH models, as it has demonstrated superior performance in previous empirical studies in terms of fit, forecasting volatility, and evaluating tail risk measures such as Value-at-Risk and Expected Shortfall. The book also explores an extension of the basic stochastic volatility model, incorporating a skewed return error distribution and a realized volatility measurement equation. The concept of realized volatility, a newly established estimator of volatility using intraday returns data, is introduced, and a comprehensive description of the resulting realized stochastic volatility model is provided. The text contains a thorough explanation of several efficient sampling algorithms for latent log volatilities, as well as an illustration of parameter estimation and volatility prediction through empirical studies utilizing various asset return data, including the yen/US dollar exchange rate, the Dow Jones Industrial Average, and the Nikkei 225 stock index. This publication is highly recommended for readers with an interest in the latest developments in stochastic volatility models and realized stochastic volatility models, particularly in regards to financial risk management.
Stochastic Volatility In Financial Markets
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Author : Antonio Mele
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic Volatility In Financial Markets written by Antonio Mele 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 2012-12-06 with Business & Economics categories.
Stochastic Volatility in Financial Markets presents advanced topics in financial econometrics and theoretical finance, and is divided into three main parts. The first part aims at documenting an empirical regularity of financial price changes: the occurrence of sudden and persistent changes of financial markets volatility. This phenomenon, technically termed `stochastic volatility', or `conditional heteroskedasticity', has been well known for at least 20 years; in this part, further, useful theoretical properties of conditionally heteroskedastic models are uncovered. The second part goes beyond the statistical aspects of stochastic volatility models: it constructs and uses new fully articulated, theoretically-sounded financial asset pricing models that allow for the presence of conditional heteroskedasticity. The third part shows how the inclusion of the statistical aspects of stochastic volatility in a rigorous economic scheme can be faced from an empirical standpoint.
Stochastic Filtering With Applications In Finance
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Author : Ramaprasad Bhar
language : en
Publisher: World Scientific
Release Date : 2010-08-19
Stochastic Filtering With Applications In Finance written by Ramaprasad Bhar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-19 with Business & Economics categories.
This book provides a comprehensive account of stochastic filtering as a modeling tool in finance and economics. It aims to present this very important tool with a view to making it more popular among researchers in the disciplines of finance and economics. It is not intended to give a complete mathematical treatment of different stochastic filtering approaches, but rather to describe them in simple terms and illustrate their application with real historical data for problems normally encountered in these disciplines. Beyond laying out the steps to be implemented, the steps are demonstrated in the context of different market segments. Although no prior knowledge in this area is required, the reader is expected to have knowledge of probability theory as well as a general mathematical aptitude.Its simple presentation of complex algorithms required to solve modeling problems in increasingly sophisticated financial markets makes this book particularly valuable as a reference for graduate students and researchers interested in the field. Furthermore, it analyses the model estimation results in the context of the market and contrasts these with contemporary research publications. It is also suitable for use as a text for graduate level courses on stochastic modeling.
Linear Quadratic Term Structure Models Toward The Understanding Of Jumps In Interest Rates
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Author : George J. Jiang
language : en
Publisher:
Release Date : 2012
Linear Quadratic Term Structure Models Toward The Understanding Of Jumps In Interest Rates written by George J. Jiang 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.
In this paper, we propose a unifying class of affine-quadratic term structure models (AQTSMs) in the general jump-diffusion framework. Extending existing term structure models, the AQTSMs incorporate random jumps of stochastic intensity in the short rate process. Using information from the Treasury futures market, we propose a GMM approach for the estimation of the risk-neutral process. A distinguishing feature of the approach is that the time series estimates of stochastic volatility and jump intensity are obtained, together with model parameter estimates. Our empirical results suggest that stochastic jump intensity significantly improves the model fit to the term structure dynamics. We identify a stochastic jump intensity process that is negatively correlated with interest rate changes. Overall, negative jumps tend to have a larger size than positive ones. Our empirical results also suggest that, at monthly frequency, while stochastic volatility has certain predictive power of inflation, jumps are neither triggered by nor predictive of changes in macroeconomic variables. At daily frequency, however, we document interesting patterns for jumps associated with informational shocks in the financial market.
Stochastic Modelling In Finance
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Author : Chaminda Hasitha Baduraliya
language : en
Publisher:
Release Date : 2012
Stochastic Modelling In Finance written by Chaminda Hasitha Baduraliya 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 trading of financial derivatives and products in financial markets has influenced the development of the world economy. Over the last few decades, a rapid growth in complex financial systems, which can generate unstable conditions in financial markets, has been observed. Therefore models are being developed to study and examine the uncertainty surrounding these financial systems in different circumstances. The important milestone of this work can be traced to the Black-Scholes formula for option pricing which was published in 1973 and revolutionized the financial industry by introducing the no-arbitrage principle [8]. This model assumed that the average rates of return and volatility are constant, however, this is not realistic. Therefore, several models have been developed, based on pragmatic studies, which generalize the Black-Scholes formula to acquire more knowledge for these financial systems. In this project, we will focus on Stochastic Differential Equations (SDEs) models in finance which do not have explicit solutions so far. In particular, Lewis [47] developed the mean-reverting-theta processes which can not only model the volatility but also the asset price. Therefore, we will establish the Euler-Maruyama (EM) numerical schemes to approximate the solution to this model and show that the EM approximate solution will converge in probability to the true solution under certain conditions. The convergence property of the corresponding step process will be examined under the same conditions to determine its application in finance. In addition, the Markov-switching format of this model can be used to explain some erratic situations observed in financial data. Under the same conditions on parameters of mean-reverting-theta model, the Markov-switching model will be examined to show that the EM approximate solution to this model will converge in probability to the true solution. Although previous models fit to a certain type of financial data, they can not be used to explain behaviour of the unpredictable abrupt structural changes in financial markets. However, the mean-reverting-theta stochastic volatility model driven by a Poisson jump process explains some of this phenomenon. Therefore, we will examine the analytical properties of EM approximate solutions to this model for two conditions of the parameters theta and beta. Since it is possible to obtain a more generalized formula for this stochastic volatility jump process, by incorporating a hybrid concept into this SDE model, we will consider the mean-reverting-theta volatility model with Poisson jumps driven by two independent Markov processes. Existing financial instruments are not strong enough to examine the convergence property of the approximate solution to this model. Therefore, we will establish EM approximate solutions to this model and examine their convergence property, when we assume similar parameter conditions to the mean-reverting-theta model. Finally, we will show that these approximate solutions of the SDE models can be used to evaluate financial quantities, options and bonds for example.