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Author: Peter Christoffersen
Publisher:
ISBN:
Category :
Languages : en
Pages : 39
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Book Description
Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the resulting biases. We investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on Samp;P 500 returns. Finally, we employ nonlinear least squares on a panel of option data. In comparison with earlier studies that explicitly solve the filtering problem, we analyze a more comprehensive option data set. The scope of our analysis is feasible because of our use of the particle filter. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, the best of the alternative volatility specifications is a model with linear rather than square root diffusion for variance which we refer to as the VAR model. This model captures the stylized facts in realized volatilities, it performs well in fitting various samples of index returns, and it has the lowest option implied volatility mean squared errors in- and out-of-sample.
Author: Peter Christoffersen
Publisher:
ISBN:
Category :
Languages : en
Pages : 39
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Book Description
Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the resulting biases. We investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on Samp;P 500 returns. Finally, we employ nonlinear least squares on a panel of option data. In comparison with earlier studies that explicitly solve the filtering problem, we analyze a more comprehensive option data set. The scope of our analysis is feasible because of our use of the particle filter. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, the best of the alternative volatility specifications is a model with linear rather than square root diffusion for variance which we refer to as the VAR model. This model captures the stylized facts in realized volatilities, it performs well in fitting various samples of index returns, and it has the lowest option implied volatility mean squared errors in- and out-of-sample.
Author: Garland Durham
Publisher:
ISBN:
Category :
Languages : en
Pages : 61
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Book Description
Understanding both the dynamics of volatility as well as the shape of the distribution of returns conditional on the volatility state are important for many financial applications. A simple single-factor SV model appears to be sufficient to capture most of the dynamics; it is the shape of the conditional distribution that is the problem. This paper examines the idea of modeling this distribution as a discrete mixture of normals. The flexibility of this class of distributions provides a transparent look into the tails of the returns distribution. Model diagnostics suggest that the model, SV-mix, does a good job of capturing the salient features of the data. In a direct comparison against several affine-jump models, SV-mix is strongly preferred by Akaike and Schwarz information criteria.
Author: Carl Chiarella
Publisher:
ISBN:
Category :
Languages : en
Pages : 25
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Book Description
This paper seeks to model the adjustment process in the stock market by a continuous time state space model focusing on input-out relations. The value of the Samp;P 500 is generated as the output of the model with earnings and the interest rate as input. The model is found to fit the data well, and indicates that the stock price dynamics can be considered as a price-following-value process. The value determines the time varying trend of price, and random buy-sell pressure drives price fluctuations about value. The 1987 stock price bubble shows up clearly as a gap between price and value.
Author: Hanxue Yang
Publisher:
ISBN:
Category :
Languages : en
Pages : 34
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Book Description
Relatively little is known about the empirical performance of infinite-activity Levy jump models, especially with non-affine volatility dynamics. We use extensive empirical data sets to study how infinite-activity Variance Gamma and Normal Inverse Gaussian jumps with affine and non-affine volatility dynamics improve goodness of fit and option pricing performance. With Markov Chain Monte Carlo, different model specifications are estimated using the joint information of the S&P 500 index and the VIX. Our paper provides clear evidence that a parsimonious non-affine model with Normal Inverse Gaussian return jumps and a linear variance specification is particularly competitive, even during the recent crisis.
Author: Sílvia Gonçalves
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of fitting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, recent empirical evidence suggests that the parameters characterizing the IVS change over time. In this paper, we study whether the resulting predictability patterns in the IVS coefficients may be exploited in practice. We propose a two-stage approach to modeling and forecasting the Samp;P 500 index options IVS. In the first stage, we model the surface along the cross-sectional moneyness and time-to-maturity dimensions, similarly to Dumas, et. al., (1998). In the second-stage, we model the dynamics of the cross-sectional first-stage implied volatility surface coefficients by means of vector autoregression models. We find that not only the Samp;P 500 implied volatility surface can be successfully modeled, but also that its movements over time are highly predictable in a statistical sense. We then examine the economic significance of this statistical predictability with mixed findings. Whereas profitable delta-hedged positions can be set up that exploit the dynamics captured by the model under moderate transaction costs and when trading rules are selective in terms of expected gains from the trades, most of this profitability disappears when we increase the level of transaction costs and trade multiple contracts off wide segments of the IVS. This suggests that predictability of the time-varying Samp;P 500 implied volatility surface may be not inconsistent with market efficiency.
Author: Nikolaos Panigirtzoglou
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
This paper presents a new approach to modeling the dynamics of implied distributions. First, we obtain a parsimonious description of the dynamics of the Samp;P 500 implied cumulative distribution functions (CDFs) by applying Principal Components Analysis. Subsequently, we develop new arbitrage-free Monte-Carlo simulation methods that model the evolution of the whole distribution through time as a diffusion process. Our approach generalizes the conventional approaches of modeling only the first two moments as diffusion processes, and it has important implications for smile-consistent option pricing and for risk management. The out-of-sample performance within a Value-at-Risk framework is examined.
Author: Gerald P. Dwyer
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We use a cost of carry model with nonzero transactions costs to motivate estimation of a nonlinear dynamic relationship between the Samp;P 500 futures and cash indexes. Discontinuous arbitrage suggests that a threshold error correction mechanism may characterize many aspects of the relationship between the futures and cash indexes. We use minute by minute data on the Samp;P 500 futures and cash indexes. The results indicate that nonlinear dynamics are important and related to arbitrage, and suggest that arbitrage is associated with more rapid convergence of the basis to the cost of carry than would be indicated by a linear model.
Author: Andrew C. Harvey
Publisher: Cambridge University Press
ISBN: 1107034728
Category : Business & Economics
Languages : en
Pages : 281
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Book Description
The volatility of financial returns changes over time and, for the last thirty years, Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have provided the principal means of analyzing, modeling and monitoring such changes. Taking into account that financial returns typically exhibit heavy tails - that is, extreme values can occur from time to time - Andrew Harvey's new book shows how a small but radical change in the way GARCH models are formulated leads to a resolution of many of the theoretical problems inherent in the statistical theory. The approach can also be applied to other aspects of volatility. The more general class of Dynamic Conditional Score models extends to robust modeling of outliers in the levels of time series and to the treatment of time-varying relationships. The statistical theory draws on basic principles of maximum likelihood estimation and, by doing so, leads to an elegant and unified treatment of nonlinear time-series modeling.
Author: Andreas Weigend
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
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Book Description
Most approaches in forecasting merely try to predict the next value of the time series.In contrast, this paper presents a framework to predict the full probability distribution. Itis expressed as a mixture model: the dynamics of the individual states is modeled with so-calledquot;expertsquot; (potentially nonlinear neural networks), and the dynamics between the states is modeledusing a hidden Markov approach. The full density predictions are obtained by a weighted superpositionof the individual densities of each expert. This model class is called quot;hidden Markov expertsquot;.Results are presented for daily Samp;P500 data. While the predictive accuracy of the mean doesnot improve over simpler models, evaluating the prediction of the full density shows a clear out-of-sampleimprovement both over a simple GARCH(1,l) model (which assumes Gaussian distributedreturns) and over a quot;gated expertsquot; model (which expresses the weighting for each state non-recursivelyas a function of external inputs). Several interpretations are given: the blending ofsupervised and unsupervised learning, the discovery of hidden states, the combination of forecasts,the specialization of experts, the removal of outliers, and the persistence of volatility.
Author: Cheng Few Lee
Publisher: World Scientific
ISBN: 9811202400
Category : Business & Economics
Languages : en
Pages : 5053
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Book Description
This four-volume handbook covers important concepts and tools used in the fields of financial econometrics, mathematics, statistics, and machine learning. Econometric methods have been applied in asset pricing, corporate finance, international finance, options and futures, risk management, and in stress testing for financial institutions. This handbook discusses a variety of econometric methods, including single equation multiple regression, simultaneous equation regression, and panel data analysis, among others. It also covers statistical distributions, such as the binomial and log normal distributions, in light of their applications to portfolio theory and asset management in addition to their use in research regarding options and futures contracts.In both theory and methodology, we need to rely upon mathematics, which includes linear algebra, geometry, differential equations, Stochastic differential equation (Ito calculus), optimization, constrained optimization, and others. These forms of mathematics have been used to derive capital market line, security market line (capital asset pricing model), option pricing model, portfolio analysis, and others.In recent times, an increased importance has been given to computer technology in financial research. Different computer languages and programming techniques are important tools for empirical research in finance. Hence, simulation, machine learning, big data, and financial payments are explored in this handbook.Led by Distinguished Professor Cheng Few Lee from Rutgers University, this multi-volume work integrates theoretical, methodological, and practical issues based on his years of academic and industry experience.
