# Browsing by Author "Tauchen, George"

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Item Open Access A New Class of Stochastic Volatility Models with Jumps: Theory and Estimation(1999) Chernov, Mikhail; Gallant, A Ronald; Ghysels, Eric; Tauchen, GeorgeThe 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 S&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.Item Open Access Essays on the Econometrics of Option Prices(2014) Vogt, ErikThis dissertation develops new econometric techniques for use in estimating and conducting inference on parameters that can be identified from option prices. The techniques in question extend the existing literature in financial econometrics along several directions.

The first essay considers the problem of estimating and conducting inference on the term structures of a class of economically interesting option portfolios. The option portfolios of interest play the role of functionals on an infinite-dimensional parameter (the option surface indexed by the term structure of state-price densities) that is well-known to be identified from option prices. Admissible functionals in the essay are generalizations of the VIX volatility index, which represent weighted integrals of options prices at a fixed maturity. By forming portfolios for various maturities, one can study their term structure. However, an important econometric difficulty that must be addressed is the illiquidity of options at longer maturities, which the essay overcomes by proposing a new nonparametric framework that takes advantage of asset pricing restrictions to estimate a shape-conforming option surface. In a second stage, the option portfolios of interest are cast as functionals of the estimated option surface, which then gives rise to a new, asymptotic distribution theory for option portfolios. The distribution theory is used to quantify the estimation error induced by computing integrated option portfolios from a sample of noisy option data. Moreover, by relying on the method of sieves, the framework is nonparametric, adheres to economic shape restrictions for arbitrary maturities, yields closed-form option prices, and is easy to compute. The framework also permits the extraction of the entire term structure of risk-neutral distributions in closed-form. Monte Carlo simulations confirm the framework's performance in finite samples. An application to the term structure of the synthetic variance swap portfolio finds sizeable uncertainty around the swap's true fair value, particularly when the variance swap is synthesized from noisy long-maturity options. A nonparametric investigation into the term structure of the variance risk premium finds growing compensation for variance risk at long maturities.

The second essay, which represents joint work with Jia Li, proposes an econometric framework for inference on parametric option pricing models with two novel features. First, point identification is not assumed. The lack of identification arises naturally when a researcher only has interval observations on option quotes rather than on the efficient option price itself, which implies that the parameters of interest are only partially identified by observed option prices. This issue is solved by adopting a moment inequality approach. Second, the essay imposes no-arbitrage restrictions between the risk-neutral and the physical measures by nonparametrically estimating quantities that are invariant to changes of measures using high-frequency returns data. Theoretical justification for this framework is provided and is based on an asymptotic setting in which the sampling interval of high frequency returns goes to zero as the sampling span goes to infinity. Empirically, the essay shows that inference on risk-neutral parameters becomes much more conservative once the assumption of identification is relaxed. At the same time, however, the conservative inference approach yields new and interesting insights into how option model parameters are related. Finally, the essay shows how the informativeness of the inference can be restored with the use of high frequency observations on the underlying.

The third essay applies the sieve estimation framework developed in this dissertation to estimate a weekly time series of the risk-neutral return distribution's quantiles. Analogous quantiles for the objective-measure distribution are estimated using available methods in the literature for forecasting conditional quantiles from historical data. The essay documents the time-series properties for a range of return quantiles under each measure and further compares the difference between matching return quantiles. This difference is shown to correspond to a risk premium on binary options that pay off when the underlying asset moves below a given quantile. A brief empirical study shows asymmetric compensation for these return risk premia across different quantiles of the conditional return distribution.

Item Open Access Estimation of Financial Models Using Moment Conditions Defined on Frequency Domain(2012) Grynkiv, IarynaThis dissertations presents the estimation methods of financial models for which the density function is not known in closed form, but the characteristic function (or Laplace transform) is available in the analytical form. In this case the estimation is done via Generalized Method of Moments, where moment conditions are defined on frequency domain. The dissertation consists of three chapters. The first chapter develops a method of selection of finite set of moment conditions out of infinite number of possibilities using proposed optimality criterion. The second chapter describes the estimation of parametric asset price models using finite set of moment conditions based on characteristic function. The final chapter proposes a method for estimating parametric models for stochastic volatility using moment conditions based on the integrated Laplace transforms.

Chapter 2 develops a new estimator for the case where the moment function is the difference between model-implied and data-implied characteristic functions. There is an optimal GMM estimator that attains the Cramer-Rao lower bound and uses all continuum of moment conditions. However, the implementation of continuum moments GMM is not practical. I develop a practical and consistent procedure to select small finite subset of moment conditions that yields a nearly efficient estimator. The moment selection algorithm works by approximating the span of the continuum of moment conditions by an optimal finite subset. The method involves a metric to evaluate how close the asymptotic variance is to the maximum likelihood estimator asymptotic variance in relative terms. The Monte Carlo application for a jump-diffusion model indicates that it is enough to use 9 moment conditions to have almost efficient estimator.

Chapter 3 is co-authored with Professor George Tauchen. We present parametric estimation of models for stock returns by describing price dynamic as the sum of two independent L'{e}vy components. The increments (moves) are viewed as discrete-time log price changes that follow an infinitely divisible distribution, i.e. stationary and independent price changes (zero drift) that follow a L'evy-type distribution. We explore empirical plausibility of two parametric models: Jump-Diffusion (C-J) and pure jump model (TS-J). The first component of each model describes the dynamics of small frequent moves and is modeled by Brownian motion in C-J model and by tempered stable L'evy process in TS-J model. The second component is responsible for big rare moves in asset prices and is modeled by compound Poisson process in both models. Using high frequency data on 13 stocks of different market capitalization for 2006-2008 sample period we find that C-J model performs well only for large cap stocks, while medium cap stock dynamics are captured by TS-J model.

Chapter 4 is co-authored with Professor George Tauchen and Professor Viktor Todorov. We propose analytically tractable way to estimate parametric models for unobserved stochastic volatility. The estimation works my matching moments of the integrated joint Laplace Transform of volatility with those implied by parametric volatility model. We use so-called Realized Laplace Transform of volatility to receive a model-free and jump-robust estimate of integrated empirical Laplace transform of the unobservable volatility. Monte Carlo reveals the proposed estimation method is very efficient. Empirical application using the method reveals that market volatility has both persistent and transient volatility spikes and both of them are sufficiently volatile which necessitates rich jump specifications to capture the observed patterns in stochastic volatility.

Item Open Access Financial Market Volatility and Jumps(2007-05-07T19:07:04Z) Huang, XinThis dissertation consists of three related chapters that study financial market volatility, jumps and the economic factors behind them. Each of the chapters analyzes a different aspect of this problem. The first chapter examines tests for jumps based on recent asymptotic results. Monte Carlo evidence suggests that the daily ratio z-statistic has appropriate size, good power, and good jump detection capabilities revealed by the confusion matrix comprised of jump classification probabilities. Theoretical and Monte Carlo analysis indicate that microstructure noise biases the tests against detecting jumps, and that a simple lagging strategy corrects the bias. Empirical work documents evidence for jumps that account for seven percent of stock market price variance. Building on realized variance and bi-power variation measures constructed from high-frequency financial prices, the second chapter proposes a simple reduced form framework for modelling and forecasting daily return volatility. The chapter first decomposes the total daily return variance into three components, and proposes different models for the different variance components: an approximate long-memory HAR-GARCH model for the daytime continuous variance, an ACH model for the jump occurrence hazard rate, a log-linear structure for the conditional jump size, and an augmented GARCH model for the overnight variance. Then the chapter combines the different models to generate an overall forecasting framework, which improves the volatility forecasts for the daily, weekly and monthly horizons. The third chapter studies the economic factors that generate financial market volatility and jumps. It extends the recent literature by separating market responses into continuous variance and discontinuous jumps, and differentiating the market’s disagreement and uncertainty. The chapter finds that there are more large jumps on news days than on no-news days, with the fixed-income market being more responsive than the equity market, and non-farm payroll employment being the most influential news. Surprises in forecasts impact volatility and jumps in the fixed-income market more than the equity market, while disagreement and uncertainty influence both markets with different effects on volatility and jumps. JEL classification: C1, C2, C5, C51, C52, F3, F4, G1, G14Item Open Access Inference in Poorly Identified Econometric Settings with Applications in Financial Economics(2017) Davies, RobertThis dissertation develops several techniques for conducting estimation and inference in non-standard econometric settings. It does so with a particular interest in applying these methods to applications in financial economics. By doing so this dissertation extends the literatures in financial economics and econometrics.

The first chapter develops econometric tools for studying the jump dependencies between the underlying or latent spot volatilities of two assets from high-frequency observations on a fixed time interval -- with a particular interest in the relationship between the individual volatilities of traded assets and the volatilities of aggregate risk factors such as the market volatility. The chapter derives an asymptotically valid test for the stability of a linear volatility jump relationship between these assets and proposes an asymptoticly valid and consistent likelihood based estimator for the beta in such relationships. The estimation context is made especially challenging because the error shrinks at a rate much slower than the standard root-n parametric rate. To conduct inference the chapter proposes a bootstrap procedure together with a justification of its asymptotic validity. Finally, the chapter considers three empirical applications of the methods and an extension on how to incorporate a Bayesian prior.

The second chapter, which represents joint work with George Tauchen, develops a method to select the threshold in threshold-based jump detection methods. The method is motivated by an analysis of threshold-based jump detection methods in the context of jump-diffusion models. The chapter shows that over the range of sampling frequencies a researcher is most likely to encounter that the usual in-fill asymptotics provide a poor guide for selecting the jump threshold. Because of this we develop a sample-based method. Our method estimates the number of jumps over a grid of thresholds and selects the optimal threshold at what we term the `take-off' point in the estimated number of jumps. The chapter show that this method consistently estimates the jumps and their indices as the sampling interval goes to zero. In several Monte Carlo studies we evaluate the performance of our method based on its ability to accurately locate jumps and its ability to distinguish between true jumps and large diffusive moves. In one of these Monte Carlo studies we evaluate the performance of our method in a jump regression context. Finally, we apply our method in two empirical studies. In one we estimate the number of jumps and report the jump threshold our method selects for three commonly used market indices. In the other empirical application we perform a series of jump regressions using our method to select the jump threshold.

The third chapter proposes a model and framework for forecasting the high-frequency analogue of two widely used tail risk measures: the value at risk and the expected shortfall. It does so by using the theory and literature on high-frequency asset price processes to motivate a particular pure-jump semimartingale forecasting model of high-frequency asset returns and thereby high-frequency value at risk and expected shortfall forecasts. Contrasted with methods developed to forecast daily values at risk and expected shortfalls this model provides a substantial improvement in the forecasting of high-frequency expected shortfalls and a modest, although still significant, improvement in the forecasting of high-frequency values at risk.

Finally, the fourth chapter develops a method for modeling high-frequency asset prices. It does so by showing how asset prices might be transformed into Levy processes. Once in the class of Levy processes this chapter develops a novel estimation procedure and a novel test of a model's specification by performing the estimation and testing over a suitably chosen family of weighting functions. An empirical study fits a selection of asset returns to two classes of Levy processes; and, finally, a detailed empirical exercise develops a flexible method to calculate intraday values at risk up to any within day horizon. A backtest of the intraday values at risk show their coverage to be right in line with the theoretical correct values.

Item Open Access New Minimum Chi-Square Methods in Empirical Finance(1996-04) Tauchen, GeorgeItem Open Access "Nonlinear Dynamic Structures"(Econometrica, 1993-07) Gallant, A Ronald; Rossi, Peter E; Tauchen, GeorgeItem Restricted "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications"(Econometrica, 1989-09) Gallant, A Ronald; Tauchen, GeorgeItem Open Access Specification Analysis of Continuous Time Models in Finance(1995-10) Gallant, A Ronald; Tauchen, GeorgeItem Open Access Using High-Frequency Options Data to Evaluate Economic Trading Models(2020) Ferreira Pelucio Salome, GuilhermeThis dissertation provides an empirical assesment of economic models based on high-frequency options data. Options data allows for the investigation of heterogeneous eﬀects across moneyness and maturities, and the use of high-frequency data makes it possible to compute various estimates at higher frequencies and analyze the data behaviour around jumps.

The ﬁrst chapter analyzes the implications of a disagreement model in which investors observe public information but agree to disagree about its interpretation. In this framework, the disagreement between investors can be recovered from the relationship between an asset’s trading volume and its volatility. Using high-frequency data for options on the S&P 500 index, I provide new empirical evidence of disagreement between investors in the market of S&P 500 index options. The options market provides two natural variables that are sharply related to disagreement: moneyness and tenor. I argue that these variables relate to disagreement about the distribution of the market index at diﬀerent quantiles and at diﬀerent times.

I extract the relationship between volume and volatility for options with diﬀerent moneyness and expirations. I ﬁnd evidence of little disagreement among investors, based on options that are at-the-money and near expiration. This evidence can be interpreted as investors’ having little disagreement about new information as it relates to the center of the distribution of returns over the short-run. From options that are far-from-the-money and with longer expirations, I ﬁnd evidence of disagreement among investors. This disagreement increases as options get away from the money, indicating that investors have higher disagreement about rare events. There is also evidence that disagreement increases with the time to expiration of options, indicating that investors have higher disagreement about events farther into the future.

The second chapter examines a general 3-factor options pricing model. This model includes the usual factors that account for short-term and long-term volatility, but also a novel factor that drives the distribution of jump returns. The novel factor, known as the tail factor, impacts the probability of future jump returns, inﬂuencing not only the price of the underlying asset, but also the behaviour of its volatility. The second chapter investigates the plausibility of this tail factor.

To investigate the plausibility of the tail factor, I recover moments of the risk-neutral distribution of market returns. The risk-neutral moments are directly related to the implications of the 3-factor pricing model and the impact of the tail factor. The tail factor jumps whenever there are jumps in the underlying asset, but it can also have independent jumps. The model implies that these diﬀerent types of jump will have diﬀerent impacts on the risk-neutral moments. Indeed, the main implication is that price jumps lead to jumps in all risk-neutral moments of order two and higher. However, idiosyncratic jumps in the tail factor lead only to jumps in moments of order three and higher. I test these implications using high-frequency options data, which allow for the computation of the risk-neutral moments of the S&P 500 index in a model-free fashion and also at higher frequency. I ﬁnd evidence of large and frequent moves in all of the computed risk-neutral moments, far in excess to the number of jumps in the market index. These large moves are in part due to jumps in the market index, that lead to co-jumps in all of the risk-neutral moments. However, the majority of large moves occur in the moments of order higher than three, consistent with the idea of jumps in the tail factor. The existence of the tail factor is further supported by co-jump tests, that reveal co-jumps between the higher order moments that are unrelated to jumps in the market index.

The last chapter examines a common assumption of many well known options pricing models: price jumps bear no impact on volatility. To examine the assumption, I analyze high-frequency moves in the market index and in the implied volatility from the options market. Speciﬁcally, I estimate jump regressions of changes in the implied volatility at times when the makret index jumps. To do so, I use high-frequency data on options and on the S&P 500 index, coupled with jump identiﬁcation techniques and a valid inference for jump regressions.

The jump regressions indicate a negative correlation between jumps in the market index and changes in the implied volatility. The estimates indicate that a market crash of 100 basis points would lead to an increase of 450 basis points in the implied volatility of options. The negative correlation is stable for options with diﬀerent moneyness and is stronger for out-of-the-money options. This indicates that the eﬀect of price jumps is diﬀerent for options that are close-to-the-money and for options that are out-of-the-money, inline with the idea of the volatility smirk. The empirical evidence from the jump regressions can be contrasted to the theoretical implications of options pricing models, such as Merton (1976) and, more recently, Andersen et al. (2015c). Merton’s model states that jumps in the underlying have no eﬀect in options’ implied volatility, while the AFT model states that only positive price jumps do not have an impact. Both models are contradicted by the empirical evidence presented in this chapter: both positive and negative jumps in the market index have an impact on the implied volatility.