MEDDAHI Nour

In this thesis, we study the various impacts of model misspecification and examine how to manage model uncertainty. We analyze the impact of ignoring fat tails on a forecast comparison test result in the first chapter, and then study the effects of ignoring the dynamics of the risk premium of returns on the amount of bank capital requirements in the second chapter. The third chapter provides a robust way to determine capital requirements in the face of model uncertainty, i.e., a lack of knowledge of the true data generation process. In the first chapter, we analyze forecast comparison tests under fat tails. Forecast comparison tests are widely used to compare the performance of two or more competing forecasts. The critical value is often obtained by the classical central limit theorem (CLT) or by the stationary bootstrap (Politis and Romano, 1994) with regularity conditions, including the one where the second moment of the loss difference is bounded. We show that if the moment condition is violated, the size of the test using classical normal asymptotics can be strongly distorted. As an alternative approach, we propose to use a "subsampling" method (Politis, Romano and Wolf, 1999) robust to heavy tails. In the empirical study, we analyze several variance prediction tests. By examining several estimators of the tail index, we show that the second moment of the loss difference is likely to be unbounded, especially when the popular squared error function is used as the loss function. We also find that the test result may change if "subsampling" is used. The second chapter explores the effect of misspecification in the conditional mean dynamics on the determination of bank capital requirements. In Basel II, capital requirements for market risk are determined based on a risk measure called Value-at-Risk (VaR). When VaR is calculated, it is often assumed that the conditional average return on an asset is constant over time. However, it is well documented that the predictability of returns increases as the forecast horizon lengthens. The contribution of this chapter is to demonstrate the problems associated with ignoring the conditional mean dynamics when we calculate VaR. We find that although models with constant and time-varying conditional mean may be statistically indistinguishable, the implied VaR may differ. This result then raises another question about how to produce VaR when one recognizes the time variability of the conditional mean but there is uncertainty about its current value. The third chapter proposes a solution to the question raised in the second chapter by examining a robust way to determine capital requirements. We propose to determine capital reserves on a worst-case basis. That is, we choose the maximum value in a set of ES forecasts mapped from the forecaster's pre-selected set of models. Assuming that the risk premium is taken to be non-negative, we show that robust ES can in fact be achieved with a model in which the conditional mean is constant and the risk premium is always zero. This finding serves as an answer to the question raised in Chapter 2 and justifies assuming a constant conditional mean.

Nowadays, a common method to forecast integrated variance is to use the fitted value of a simple OLS autoregression of the realized variance. However, non-parametric estimates of the tail index of this realized variance process reveal that its second moment is possibly unbounded. In this case, the behavior of the OLS estimators and the corresponding statistics are unclear. We prove that when the second moment of the spot variance is unbounded, the slope of the spot variance’s autoregression converges to a random variable as the sample size diverges. The same result holds when one uses the integrated or realized variance instead of the spot variance. We then consider the class of diffusion variance models with an affine drift, a class which includes GARCH and CEV processes, and we prove that IV estimation with adequate instruments provide consistent estimators of the drift parameters as long as the variance process has a finite first moment regardless of the existence of the second moment. In particular, for the GARCH diffusion model with fat tails, an IV estimation where the instrument equals the sign of the centered lagged value of the variable of interest provides consistent estimators. Simulation results corroborate the theoretical findings of the paper.

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This thesis consists of four self-contained chapters aimed at contributing to a better understanding of asset price formation and dynamics in a consumption-based model of financial asset pricing (C-MEDAF). Chapter 1 examines the term structure of stock returns in the main C-MEDAF models and shows that allowing consumption and dividend flows to be negatively affected by volatility shocks as observed empirically ("leverage effect") could make short-term assets riskier than long-term assets as recently found in some empirical studies. This modification gives these models more flexibility to capture different forms of the term structure of risky asset rates of return while respecting the observed levels of the risk premium and the risk-free rate of return. Chapter 2 proposes a regime-switching model to accommodate the changing behavior of the slope of the term structure of risky asset returns as observed in the data. We show that such a model allows combining regime-specific properties of one-regime models such as a positive or negative average slope of the term structure of returns, and gives more flexibility in the shape of the term structure of risky asset returns. Chapter 3 studies the equity market expectations hypothesis. According to this hypothesis, current returns on long-term assets are a weighted average of the expectation of future short-term returns. This test was mainly performed on the Treasury bill market and in many cases rejected. This hypothesis is not rejected in the equity market, but future returns are also predictable. Chapter 4 examines estimation and inference in the long-run risk model using the generalized method of moments.

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The general topic of this thesis is financial risk in a context of high frequency data availability, with a particular focus on systemic risk, large portfolio risk and microstructure noise. It is organized in three main chapters. The first chapter proposes a reduced-form, continuous-time model to characterize the propagation of negative idiosyncratic shocks within a set of multiple financial entities. Using a factor model with mutually excited jumps on both prices and volatility, we distinguish different sources of financial shock transmission such as correlation, connectivity and contagion. The estimation strategy is based on the generalized method of moments and takes advantage of the availability of very high frequency data. We use specific model parameters to define weighted networks for the transmission of shocks. Also, we provide new measures of financial system fragility. We construct shock propagation maps, first for some key banks and insurance companies in the US, and then for the nine largest sectors of the US economy. The result is that, beyond common factors, financed shocks propagate through two distinct and complementary channels: prices and volatility. In the second chapter, we develop a new estimator of the realized covolatility matrix, applicable in situations where the number of assets is large and the high-frequency data are contaminated by microstructure noise. Our estimator is based on the assumption of a factor structure of the noise component, distinct from the latent systematic risk factors that characterize the cross-sectional variation in returns.The new estimator provides theoretically more efficient and accurate finite sample estimates, relative to other recent estimation methods. The theoretical and simulation-based results are corroborated by an empirical application related to portfolio allocation and risk minimization involving several hundred individual stocks. The last chapter presents a methodology for estimating microstructure noise characteristics and latent returns in a high-dimensional setting. We rely on factorial assumptions on both the latent returns and the microstructure noise. The procedure is capable of estimating common factor rotations, loading coefficients, and microstructure noise volatilities for a large number of assets. Using the stocks included in the S & P500 over the period from January 2007 to December 2011, we estimate the common factors of the microstructure noise and compare them to some market-wide liquidity measures calculated from real financial variables. The result is that: the first factor is correlated with the average spread and the average number of shares outstanding . the second and third factors are uniquely related to the spread . the fourth and fifth factors vary significantly with the average closing stock price. In addition, the volatilities of the microstructure noise factors are largely explained by the average spread, the average volume, the average number of trades and the average size of those trades.

Institutional changes in the regulation of financial markets have increased the number of markets and the simultaneous listing of assets on several markets. The prices of a security on these exchanges or of a security and its derivatives are linked by arbitrage activities. In these "informationally connected" market settings, it is of interest to regulators, investors and researchers to understand how each market contributes to the dynamics of fundamental value. This thesis develops new tools to measure the contribution, relative to frequency, of each market to price formation and volatility formation. In the first chapter, I show that existing measures of price discovery lead to misleading conclusions when using high frequency data. Due to microstructure noises, they create a confusion between the "velocity" and "noise" dimensions in the information processing. I then propose noise-robust measures that detect "which market is fast" and produce very tight bounds. Using Monte Carlo simulations and Dow Jones stocks sold on the NYSE and NASDAQ, I show that the data corroborate my theoretical conclusions. In the second chapter, I propose a new definition of price discovery by constructing a response function that estimates the permanent impact of market innovation, and I give its asymptotic distribution. This framework breaks new ground by providing testable results for innovation variance-based metrics. I then present an equilibrium model of futures markets at different maturities, and show that it supports my measure: Consistent with the theoretical findings, the measure selects the market with the most participants as dominant. An application on LME metals shows that the 3-month futures contract dominates both the cash market and the 15-month contract. The third chapter introduces a complete continuous-time framework for high-frequency analysis, as the literature exists only in discrete time. It also has advantages over the literature by explicitly dealing with microstructure noise and by incorporating stochastic volatility. An application, made on the four Dow Jones stocks listed on NASDAQ and traded on NYSE, show that NASDAQ dominates the continuous price discovery process. In the fourth chapter, while the literature focuses on prices, I develop a framework to study volatility. This helps answer questions such as: Does futures market volatility contribute more than spot market volatility to the formation of fundamental volatility? I construct a VECM with Stochastic Volatility estimated with MCMC and Bayesian inference. I show that conditional volatilities have a common factor and propose measures of volatility discovery. I apply it to daily data of metal futures and the EuroStoxx50. I find that while price formation takes place in the spot market, volatility discovery takes place in the futures market. In a second part, I construct an analysis framework that exploits High Frequency data and avoids the computational burden of MCMC. I show that the Realized Volatilities are cointegrated and calculate the contribution of the NYSE and NASDAQ to the permanent volatility of the Dow Jones stocks. I obtain that volume volatility is the best determinant of volatility discovery. But the low numbers obtained suggest the existence of other factors.

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If there is good information to forecast Treasury prices over time, how can this information be used to improve the investor's risk/reward and term structure modeling? This thesis aims to answer this question. The first chapter analyzes the predictive role of alternative measures of the liquidity premium of TIPS (Treasury Inflation-Protected Securities) over Treasury securities for excess government bond yields. The results show that the liquidity premium predicts positive (negative) excess returns for TIPS (nominal Treasury). I also find that the out-of-sample predictive power of liquidity for excess returns on nominal Treasuries appears to have been driven by the events of the recent financial crisis. On the other hand, I find empirically that there is also predictive power for out-of-sample excess TIPS yields during normal periods as well as bad periods.In the second chapter, I examine whether the TIPS liquidity premium can be considered as a so-called unspanned factor (i.e., whose value is not a linear combination of the yield curve) for predicting bond yields, but is not necessarily spanned by the U.S. yield curve. I consider an affine and Gaussian model of the term structure of zero-coupon U.S. Treasury bonds for all Treasuries and TIPS, with one unspanned factor: liquidity risk. In this model, the liquidity factor is constrained to affect only cross-sectional yields, but it does allow for the determination of bond risk premiums. Empirical evidence suggests that the liquidity factor does not affect the dynamics of bonds under risk-neutral probability, but does affect those dynamics under the historical measure. Therefore, the information contained in the yield curve proves insufficient to fully characterize the price change of curvature risk. In the third chapter, I estimate, by non-parametric methods, the optimal bond portfolio choice for a representative agent who acts in an optimal way with respect to his expected utility over the next period, from the liquidity signal observed ex ante. Considering the different measures of liquidity, I find that the liquidity differential between nominal bonds and TIPS appears to be a significant factor in the choice of the US government bond portfolio. Indeed, the conditional allocation to risky assets decreases as market liquidity conditions deteriorate, and the market liquidity effect decreases with the investment horizon. I also find that the predictability of bond returns translates into better allocation and performance both within and outside the sample.

The relationship between conditional volatility and expected stock market returns, the so-called riskreturn trade-off, has been studied at high- and low-frequency. We propose an asset pricing model with generalized disappointment aversion preferences and short- and long-run volatility risks that captures several stylized facts associated with the risk-return trade-off at short and long horizons. Writing the model in Bonomo et al. (2011) at the daily frequency, we aim at reproducing the moments of the variance premium and realized volatility, the long-run predictability of cumulative returns by the past cumulative variance, the short-run predictability of returns by the variance premium, as well as the daily autocorrelation patterns at many lags of the VIX and of the variance premium, and the daily crosscorrelations of these two measures with leads and lags of daily returns. By keeping the same calibration as in this previous paper, we ensure that the model is capturing the first and second moments of the equity premium and the risk-free rate, and the predictability of returns by the dividend yield. Overall adding generalized disappointment aversion to the Kreps–Porteus specification improves the fit for both the short-run and the long-run risk-return trade-offs.

This thesis presents several extensions to positive affine interest rate models. A first chapter introduces the concepts related to the models used in the following chapters. It details the definition of so-called affine processes, and the construction of asset price models obtained by non-arbitrage. Chapter 2 proposes a new estimation and filtering method for linear-quadratic state-space models. The next chapter applies this estimation method to the modeling of interbank spreads in the Eurozone, in order to decompose the fluctuations related to default and liquidity risk. Chapter 4 develops a new technique to create multivariate affine processes from their univariate counterparts, without imposing conditional independence between their components. The last chapter applies this method and derives a multivariate affine process in which some components can remain at zero for extended periods. Incorporated into an interest rate model, this process can efficiently account for zero-bottom rates.

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This thesis is composed of three independent chapters stemming from a common problem: to build econometric specifications of the dynamics of financial markets, integrating a structural modeling of informational aspects. The first chapter is devoted to the frequency of transactions on financial markets in the presence of asymmetric information. We consider a Kyle (1985) model, but where liquidity shocks do not always occur. We characterize the set of perfect Bayesian equilibria. In particular, we show that the insider does not systematically intervene in the market, which affects the trading frequencies. We then extend this analysis to the case where volumes are heterogeneous. The second chapter focuses on the temporal aggregation of volatility. We propose a class of models of conditional variance that includes most of the models existing in the literature where the variance is linear (Garch, linear factors). We show that this class is robust to temporal and individual aggregation and marginalization. We also show the superiority and relevance of this class compared to the so-called "weak arch" class in terms of financial and statistical interpretations. We establish the direct link between our class and the class of continuous time processes called "stochastic volatility". Finally, the last chapter is devoted to the estimation of models defined by their conditional mean and variance, in particular those of the arch type. We consider a large class of m-estimators and we show the optimal estimator, which depends crucially on the conditional skewness and kurtosis coefficients. We show that it is more efficient than the pmv estimator and that it is equivalent to the optimal gmm estimator. A Monte Carlo study confirms these results.