Optimal Instrumental Variables Generators Based on Improved Hausman Regression, with an Application to Hedge Funds Returns

This paper proposes new Hausman-based estimators lying on cumulants optimal instruments. Using these new generated strong instruments in a GMM setting, we obtain new GMM estimators which we call GMM-C and its homologue, the GMM-hm. This procedure improves the method of moments for identifying the parameters of a model. Also, our study gives way to a new indicator signalling the presence of specification errors in financial models. We apply our battery of tests and estimators to a sample of 22 HFR hedge fund indices observed monthly over the period 1990-2005. Our tests reveal that specification errors corrupt parameters estimation of financial models of returns. Therefore, it is not surprising that the ranking of hedge funds is very sensitive to the choice of estimators. Our new indicator of specification errors reveals itself very powerful to detect those errors.Asset Pricing Models, specification errors, Hausman test, GMM, optimal instruments.

Risk Procyclicality and Dynamic Hedge Fund Strategies

It is well-known that traditional financial institutions like banks follow procyclical risk strategies (Rajan 2005, 2009, Shin 2009, Jacques 2010) in the sense that they increase their leverage in economic expansions and reduce it in recessions, which leads to a procyclical behaviour for their betas and other risk and financial performance measures. But it is less known that the spectrum of the returns of many hedge fund strategies displays a high volatility at business cycle frequencies. In this paper, we study this unknown stylized fact resorting to two procedures: conditional modelling and Kalman filtering of Funds alphas and betas. We find that hedge fund betas are usually procyclical. Regarding the alpha, it is often high at the beginning of a market upside cycle but as the demand pressure stems from investors, it eventually fades away, which suggests that the alpha puzzle documented in the financial literature is questionable when cast in a dynamic setting.risk measures; Aggregate risk; Financial stability; Conditional models; Kalman Filter; Spectral analysis.

"Forecasting stochastic Volatility using the Kalman filter: an application to Canadian Interest Rates and Price-Earnings Ratio"

In this paper, we aim at forecasting the stochastic volatility of key financial market variables with the Kalman filter using stochastic models developed by Taylor (1986,1994) and Nelson (1990). First, we compare a stochastic volatility model relying on the Kalman filter to the conditional volatility estimated with the GARCH model. We apply our models to Canadian short-term interest rates. When comparing the profile of the interest rate stochastic volatility to the conditional one, we find that the omission of a constant term in the stochastic volatility model might have a perverse effect leading to a scaling problem, a problem often overlooked in the literature. Stochastic volatility seems to be a better forecasting tool than GARCH(1,1) since it is less conditioned by autoregressive past information. Second, we filter the S&P500 price-earnings(P/E) ratio in order to forecast its value. To make this forecast, we postulate a rational expectations process but our method may accommodate other data generating processes. We find that our forecast is close to a GARCH(1,1) profile.Stochastic volatility, Kalman filter, P/E ratio forecast, Interest rate forecast

Forecasting stochastic Volatility using the Kalman filter: An Application to Canadian Interest Rates and Price-Earnings Ratio

In this paper, we aim at forecasting the stochastic volatility of key financial market variables with the Kalman filter using stochastic models developed by Taylor (1986, 1994) and Nelson (1990). First, we compare a stochastic volatility model relying on the Kalman filter to the conditional volatility estimated with the GARCH model. We apply our models to Canadian short-term interest rates. When comparing the profile of the interest rate stochastic volatility to the conditional one, we find that the omission of a constant term in the stochastic volatility model might have a perverse effect leading to a scaling problem, a problem often overlooked in the literature. Stochastic volatility seems to be a better forecasting tool than GARCH(1,1) since it is less conditioned by autoregressive past information. Second, we filter the S&P500 price-earnings (P/E) ratio in order to forecast its value. To make this forecast, we postulate a rational expectations process but our method may accommodate other data generating processes. We find that our forecast is close to a GARCH(1,1) profile.Stochastic volatility; Kalman filter; P/E ratio forecast; Interest rate forecast.

Forecasting Irregularly Spaced UHF Financial Data: Realized Volatility vs UHF-GARCH Models

A very promising literature has been recently devoted to the modeling of ultra-high-frequency (UHF) data. Our first aim is to develop an empirical application of Autoregressive Conditional Duration GARCH models and the realized volatility to forecast future volatilities on irregularly spaced data. We also compare the out sample performances of ACD GARCH models with the realized volatility method. We propose a procedure to take into account the time deformation and show how to use these models for computing daily VaR.Realized volatility, Ultra High Frequency GARCH, time deformation, financial markets, Daily VaR.

De l'évaluation du risque de crédit

En recourant de plus en plus aux modèles à forme réduite, la théorie de l'évaluation du risque de crédit se distance de plus en plus de l'ingénierie financière traditionnelle qui donne la part belle aux modèles structurels. Bien qu'ils postulent l'absence d'arbitrage, les modèles à forme réduite reposent sur la distribution des pertes d'une entreprise dans un monde risque-neutre plutôt que sur un processus de diffusion. Il s'ensuit que la faillite n'est pas un processus prévisible comme dans le modèle original de Merton mais survient de façon subite. L'avenir de l'évaluation du risque de crédit semble être du côté des modèles hybrides qui combinent les modèles structurels et les modèles à forme réduite.évaluation des actifs, risque de crédit, ingénierie financière.

La simulation de Monte Carlo: forces et faiblesses (avec applications Visual Basic et Matlab et présentation d’une nouvelle méthode QMC)

Monte Carlo simulation has an advantage upon the binomial tree as it can take into account the multidimensions of a problem. However it convergence speed is slower. In this article, we show how this method may be improved by various means: antithetic variables, control variates and low discrepancy sequences: Faure, Sobol and Halton sequences. We show how to compute the standard deviation of a Monte Carlo simulation when the payoffs of a claim, like a contingent claim, are nonlinear. In this case, we must compute this standard deviation by doing a great number of repeated simulations such that we arrive at a normal distribution of the results. The mean of the means of these simulations is then a good estimator of the wanted price. We also show how to combine Halton numbers with antithetic variables to improve the convergence of a QMC. That is our new version of QMC which is then well named because the result varies from one simulation to the other in our version of the QMC while the result is fixed (not random) in a classical QMC, like in the binomial tree.Financial engineering, derivatives, Monte Carlo simulation, low discrepancy sequences.

Programmes de volatilité stochastique et de volatilité implicite : applications Visual Basic (Excel) et Matlab

Markets makers quote many option categories in terms of implicit volatility. In doing so, they can reactivate the Black and Scholes model which assumes that the volatility of an option underlying is constant while it is highly variable. First of all, this article, whose purpose is very empirical, presents a simulation of stochastic volatility programmed in Visual Basic (Excel) whose aim is to compute the price of an European option written on a zero coupon bond. We compare this computed price with this one resulting from Black analytical solution and we also show how to compute an interest rate forecast with the help of the simulation model. Then we write many Visual Basic and Matlab programs for the purpose of computing the implicit volatility surface, a three-dimensional surface which can be plotted by using graphical capacities of Excel and Matlab. It remains that the concept of implicit volatility is very criticised because it is computed with the exercise price of an option and not with the price of the underlying, as it should be. Therefore, there are biases in the estimation of the «greeks» computed with implicit volatility.Financial engineering, Monte Carlo simulation, stochastic volatility, implicit volatility.

Quelques applications du filtre de Kalman en finance: estimation et prévision de la volatilité stochastique et du rapport cours-bénéfices

The popularity of Kalman filter is increasing in financial studies, notably to estimate diffusion processes. In this article, we show how we can use it to forecast the volatility of returns and the price-earnings ratio of the S&P500. The Kalman filter is consequently very versatile when variables, as volatility or forecasted price-earnings ratio, are unobserved. But the forecaster must use his judgment when he uses the Kalman filter. An error of specification in the model may give way to very biased forecasts.Kalman filter, diffusion processes, financial forecasting, financial econometrics.

L'assurance de portefeuille: Simulations en Visual Basic de portefeuilles visant à reproduire les flux monétaires de stratégies d'options

In this paper, we simulate portfolios which aim to insure the invested capital. The object of our simulations is the duplication of the cashflows of strategies based on options. We initially show how to duplicate the cash-flows of a call by using a leveraged portfolio of stocks. After, we simulate another portfolio which aims to replicate a protective put. Finally, we simulate the cushion technique of Black and analyse the sensitivity of the insured portfolio to some parameters like the degree of risk aversion of the investor. We consider the limits of each of the studied strategies.Financial Engineering; Portfolio Insurance; Monte Carlo simulation.