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27
Estimation methods for stochastic volatility models: a survey
 Journal of Economic Surveys
, 2004
"... The empirical application of Stochastic Volatility (SV) models has been limited due to the difficulties involved in the evaluation of the likelihood function. However, recently there has been fundamental progress in this area due to the proposal of several new estimation methods that try to overcome ..."
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Cited by 43 (2 self)
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The empirical application of Stochastic Volatility (SV) models has been limited due to the difficulties involved in the evaluation of the likelihood function. However, recently there has been fundamental progress in this area due to the proposal of several new estimation methods that try to overcome this problem, being at the same time, empirically feasible. As a consequence, several extensions of the SV models have been proposed and their empirical implementation is increasing. In this paper, we review the main estimators of the parameters and the volatility of univariate SV models proposed in the literature. We describe the main advantages and limitations of each of the methods both from the theoretical and empirical point of view. We complete the survey with an application of the most important procedures to the S&P 500 stock price index.
Properties of realized variance for a pure jump process: Calendar time sampling versus business time sampling
, 2004
"... Comments are welcome In this paper we study the impact of market microstructure effects on the properties of realized variance using a pure jump process for high frequency security prices. Closed form expressions for the bias and mean squared error of realized variance are derived under alternative ..."
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Cited by 31 (0 self)
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Comments are welcome In this paper we study the impact of market microstructure effects on the properties of realized variance using a pure jump process for high frequency security prices. Closed form expressions for the bias and mean squared error of realized variance are derived under alternative sampling schemes. Importantly, we show that business time sampling is generally superior to the common practice of calendar time sampling in that it leads to a reduction in mean squared error. Using IBM transaction data we estimate the model parameters and determine the optimal sampling frequency for each day in the data set. The empirical results reveal a downward trend in optimal sampling frequency over the last 4 years with considerable daytoday variation that is closely related to changes in market liquidity.
Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate
"... Abstract: We model the joint risk neutral distribution of the eurosterling and the dollarsterling exchange rates using optionimplied marginal distributions that are connected via a copula function that satisfies the triangular noarbitrage condition. We then derive a univariate distribution for ..."
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Cited by 20 (3 self)
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Abstract: We model the joint risk neutral distribution of the eurosterling and the dollarsterling exchange rates using optionimplied marginal distributions that are connected via a copula function that satisfies the triangular noarbitrage condition. We then derive a univariate distribution for a simplified sterling effective exchange rate index (ERI). Our results indicate that standard parametric copula functions, such as the commonly used Normal and Frank copulas, fail to capture the degree of asymmetry observed in the data. We overcome this problem by using a nonparametric dependence function in the form of a Bernstein copula which is shown to produce a very close fit. We further give an example of how our approach can be used to price currency index options accounting for strikedependent implied volatilities. We would like to thank Michael Bennett, Andrew Patton and Alessio Sancetta, participants at the CEF 2005 in Washington and the GFC 2005 in Dublin, as well as seminar participants at the Bank of England for useful comments and discussion. Any remaining mistakes are our own. This paper represents the views of the authors and should not be thought to represent those of the Bank of England and members of the Monetary Policy Committee. 2
Deriving the APT when the Number of Factors is Unknown
, 1999
"... This paper examines the use of proxies (or reference variables) for the true factors in the Arbitrage Pricing Theory (APT). It generalises the work of Reisman(1992) and Shanken(1992) and shows that, when there are more reference variables than the true factors, the APT still holds. The possibility o ..."
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Cited by 19 (1 self)
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This paper examines the use of proxies (or reference variables) for the true factors in the Arbitrage Pricing Theory (APT). It generalises the work of Reisman(1992) and Shanken(1992) and shows that, when there are more reference variables than the true factors, the APT still holds. The possibility of fewer reference variables than the true factors is also considered, but the APT is not shown to hold, in the same sense, for this case. This work builds on an earlier paper by Ingersoll(1984), and our propositions can be thought of as specialisations of his Theorems 1 and 6. Our work does not use the mathematics of Hilbert and Banach spaces (as used by Reisman(1992)) and, thus, is open to a much wider audience. Deriving the APT when the Number of Factors is Unknown 1
Aggregation and memory of models of changing volatility
, 2001
"... In this paper we study the effect of contemporaneous aggregation of an arbitrarily large number of processes featuring dynamic conditional heteroskedasticity with short memory when heterogeneity across units is allowed for. We look at the memory properties of the limit aggregate. General, necessary, ..."
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Cited by 18 (0 self)
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In this paper we study the effect of contemporaneous aggregation of an arbitrarily large number of processes featuring dynamic conditional heteroskedasticity with short memory when heterogeneity across units is allowed for. We look at the memory properties of the limit aggregate. General, necessary, conditions for long memory are derived. More specific results relative to certain stochastic volatility models are also developed, providing some examples of how long memory volatility can be obtained by aggregation. JEL classification: C43
Testing for OneFactor Models versus Stochastic Volatility Models Valentina Corradi and Walter DistasoTesting for OneFactor Models versus Stochastic Volatility Models ∗
, 2004
"... This paper proposes a testing procedure in order to distinguish between the case where the volatility of an asset price is a deterministic function of the price itself and the one where it is a function of one or more (possibly unobservable) factors, driven by not perfectly correlated Brownian motio ..."
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Cited by 14 (1 self)
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This paper proposes a testing procedure in order to distinguish between the case where the volatility of an asset price is a deterministic function of the price itself and the one where it is a function of one or more (possibly unobservable) factors, driven by not perfectly correlated Brownian motions. Broadly speaking, the objective of the paper is to distinguish between a generic onefactor model and a generic stochastic volatility model. In fact, no specific assumption on the functional form of the drift and variance terms is required. The proposed tests are based on the difference between two different nonparametric estimators of the integrated volatility process. Building on some recent work by Bandi and Phillips (2003) and BarndorffNielsen and Shephard (2004a), it is shown that the test statistics converge to a mixed normal distribution under the null hypothesis of a one factor diffusion process, while diverge in the case of multifactor models. The findings from a Monte Carlo experiment indicate that the suggested testing procedure has good finite sample properties.
Estimation of a microfounded herding model of German survey expectations”, Working
, 2007
"... The paper considers the dynamic adjustments of an average opinion index that can be derived from a microfounded framework where the individual agents switch between two kinds of sentiment with certain transition probabilities. The index can thus represent a general business climate, i.e., expectatio ..."
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Cited by 14 (6 self)
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The paper considers the dynamic adjustments of an average opinion index that can be derived from a microfounded framework where the individual agents switch between two kinds of sentiment with certain transition probabilities. The index can thus represent a general business climate, i.e., expectations about the future course of the economy. This approach is empirically tested with the survey expectations published by the ZEW and ifo institute. The estimated coefficients make economic sense and are highly significant. In particular, besides effects from fundamental data like the output gap in the recent past, one can identify a strong herding mechanism within both panels, such that metaphorically speaking the agents do not just join the crowd but follow each single motion of it. In addition, the transition probabilities of the ZEW agents are found to be influenced by the ifo climate but not the other way round.
A Simple Asymmetric Herding Model to Distinguish Between Stock and Foreign Exchange Markets
"... Drawing on previous work of one of the authors, the paper takes an asymmetric variant of Kirman’s ant model and combines it with an elementary asset pricing mechanism. The closedform solution of the equilibrium probability distribution allows the specification of a tractable likelihood function for ..."
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Cited by 12 (3 self)
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Drawing on previous work of one of the authors, the paper takes an asymmetric variant of Kirman’s ant model and combines it with an elementary asset pricing mechanism. The closedform solution of the equilibrium probability distribution allows the specification of a tractable likelihood function for daily returns, which is then employed to estimate the model’s behavioural parameters for a large pool of Japanese stocks. By way of Monte Carlo simulations it is found that most of these markets belong to the same class, which is characterized by a dominance of the stylized noise traders. In contrast, the model assigns a number of major foreign exchange markets to a different class, where on average the majority of agents follows the fundamentalist trading rule. Implications for the tail index are also worked out.
Transaction Taxes, Traders’ Behavior and Exchange Rate Risks
"... Abstract: We propose a new model of chartistfundamentalistinteraction in which both groups of traders are allowed to select endogenously between different forecasting models and different investment horizons. Stochastic interest rates in both countries and different behavioral assumptions for tren ..."
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Cited by 10 (1 self)
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Abstract: We propose a new model of chartistfundamentalistinteraction in which both groups of traders are allowed to select endogenously between different forecasting models and different investment horizons. Stochastic interest rates in both countries and different behavioral assumptions for trendextrapolating and fundamental based forecasts determine the agents’ market orders which drive the exchange rate. A numerical analysis of the model shows that it is able to replicate stylized facts of observed financial return time series like excess kurtosis and volatility clustering. Within this framework we study the effects of transaction taxes on exchange rate volatility and traders ’ behavior measured by their population fractions. Simulations yield the result that on the macroscopic level these taxes reduce the variance of exchange rate returns, but also increase their kurtosis. Moreover, on the microscopic level the tax harms shortterm speculation in favor of longterm investment, while it also harms trading rules based on economic
2006): “Price and Wealth Dynamics in a Speculative Market with Generic Procedurally Rational Traders,” CeNDEF Working Paper 200602
"... An agentbased model of a simple financial market with arbitrary number of traders having relatively general behavioral specifications is analyzed. In a pure exchange economy with two assets, riskless and risky, trading takes place in discrete time under endogenous price formation setting. Traders ..."
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Cited by 8 (2 self)
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An agentbased model of a simple financial market with arbitrary number of traders having relatively general behavioral specifications is analyzed. In a pure exchange economy with two assets, riskless and risky, trading takes place in discrete time under endogenous price formation setting. Traders ’ demands for the risky asset are expressed as fractions of their individual wealths, so that the dynamical system in terms of wealth and return is obtained. Agents ’ choices, i.e. investment fractions, are described by means of the generic smooth functions of an infinite information set. The choices can be consistent with (but not limited to) the solutions of the expected utility maximization problems. A complete characterization of equilibria is given. It is shown that irrespectively of the number of agents and of their behavior, all possible equilibria belong to a onedimensional “Equilibrium Market Line”. This geometric tool helps to illustrate possibility of different phenomena, like multiple equilibria, and also can be used for comparative static analysis. The stability conditions of equilibria are derived for general model specification and allow to discuss the relative performances of different strategies and the selection principle