Flexible time series models for subjective distribution estimation with monetary policy in view

In this paper, we introduce a new approach to estimate the subjective distribution of the future short rate from the historical dynamics of futures, based on a model generated by a Normal Inverse Gaussian distribution, with dynamical parameters. The model displays time varying conditional volatility, skewness and kurtosis and provides a flexible framework to recover the conditional distribution of the future rates. For the estimation, we use maximum likelihood method. Then, we apply the model to Fed Fund futures and discuss its performance.Subjective distribution - autoregressive conditional density - generalized hyperbolic distribution - Fed Funds futures contracts

Flexible time series models for subjective distribution estimation with monetary policy in view

In this paper, we introduce a new approach to estimate the subjective distribution of the future short rate from the historical dynamics of futures, based on a model generated by a Normal Inverse Gaussian distribution, with dynamical parameters. The model displays time varying conditional volatility, skewness and kurtosis and provides a flexible framework to recover the conditional distribution of the future rates. For the estimation, we use maximum likelihood method. Then, we apply the model to Fed Fund futures and discuss its performance.Subjective distribution, autoregressive conditional density, generalized hyperbolic distribution, Fed Funds futures contracts.

Further evidence on the impact of economic news on interest rates

US interest rates'overnight reaction to macroeconomic announcements is of tremendous importance trading fixed income securities. Most of the empirical studies achieved so far either assumed that the interest rates' reaction to announcements is linear or independent to the state of the economy. We investigate the shape of the tern structure reaction of the swap rates to announcements using several linear and non-linear time series models. The empirical results yield several not-so-well-known stylized facts about the bond market. First, and although we used a daily dataset, we find that the introduction of non linear models leads to the finding of a significant number of macroeconomic figures that actually produce an effect over the yield curve. Most of the studies using daily datasets did not corroborate so far this conclusion. Second, we find that the term structure response to announcements can be much more complicated that what is generally found : we noticed at least four types of patterns in the term structure reaction of interest rates across maturities, including the hump-shaped one that is generally considered. Third, by comparing the shapes of the rates' term structure reaction to announcements with the first four factors obtained when performing a principal component analysis of the daily changes in the swap rates, we propose a first interpretation and classification of these different shapes. Fourth, we find that the existence of some outliers in the one-day changes in interest rates usually leads to a strong underestimation of the reaction of interest rates to announcements, explaining the different results obtained between high-frequency and daily datasets : the first type of study seems to lead to the finding of fewer market mover announcements.Macroeconomic announcements, interest rates dynamic, outliers, reaction function, principale component analysis.

Further evidence on the impact of economic news on interest rates

US interest rates’ overnight reaction to macroeconomic announcements is of tremendous importance when trading fixed income securities. Most of the empirical studies achieved so far either assumed that the interest rates’ reaction to announcements is linear or independent to the state of the economy. We investigate the shape of the term structure reaction of the swap rates to announcements using several linear and non-linear time series models. The empirical results yield several not-so-well-known stylized facts about the bond market. First, and although we used a daily dataset, we find that the introduction of non linear models leads to the finding of a significant number of macroeconomic figures that actually produce an effect over the yield curve. Most of the studies using daily datasets did not corroborate so far this conclusion. Second, we find that the term structure response to announcements can be much more complicated that what is generally found: we noticed at least four types of patterns in the term structure reaction of interest rates across maturities, including the hump-shaped one that is generally considered. Third, by comparing the shapes of the rates’ term structure reaction to announcements with the first four factors obtained when performing a principal component analysis of the daily changes in the swap rates, we propose a first interpretation and classification of these different shapes. Fourth we find that the existence of some outliers in the one-day changes in interest rates usually leads to a strong underestimation of the reaction of interest rates to announcements, explaining the different results obtained between high-frequency and daily datasets: the first type of study seems to lead to the finding of fewer market mover announcements.Macroeconomic Announcements; Interest Rates Dynamic; Outliers; Reaction Function; Principal Component Analysis

Option Pricing under GARCH models with Generalized Hyperbolic innovations (I) : Methodology

In this paper, we present an alternative to the Black Scholes model for a discrete time economy using GARCH-type models for the underlying asset returns with Generalized Hyperbolic (GH) innovations that are potentially skewed and leptokurtic. Assuming that the stochastic discount factor is an exponential affine function of the states variables, we show that this class of distributions is stable under the Risk neutral change of probability.GARCH, Generalized Hyperbolic Distribution, pricing, risk neutral distribution.

Martingalized Historical approach for Option Pricing

In a discrete time option pricing framework, we compare the empirical performance of two pricing methodologies, namely the affine stochastic discount factor and the empirical martingale correction methodologies. Using a CAC 40 options dataset, the differences are found to be small : the higher order moment correction involved in the SDF approach may not be that essential to reduce option pricing errors.Generalized hyperbolic distribution, option pricing, incomplete market, CAC 40, Stochastic Discount Factor, martingale correction.

Do jumps help in forecasting the density of returns?.

The estimation of the jump component in asset pricing has witnessed a considerably growing body of literature. Of particular interest is the decomposition of total volatility between its continuous and jump components. Recent contributions highlight the importance of the jump component in forecasting the volatility at different horizons. In this paper, we extend the methodology developed by Maheu and McCurdy (2011) to measure the information content of intraday data in forecasting the density of returns at horizons up to sixty days. We extract jumps as in Andersen, Bollerslev, Frederiksen and Nielsen (2010) to have a measure of the jumps in returns. Then, we estimate a bivariate model of returns and volatilities where the jump component is indepen- dently modeled. Our empirical results for S&P 500 futures, WTI crude oil futures, the USD/JPY exchange rate and the MacDonald’s stock confirm the importance of considering the continuous/jump decomposition for density forecasting.bivariate model; median realized volatility; bipower variation; realized volatility; jumps; density forecasting;

Likelihood-Related Estimation Methods and Non-Gaussian GARCH Processes

This article discusses the finite distance properties of three likelihood-based estimation strategies for GARCH processes with non-Gaussian conditional distributions : (1) the maximum likelihood approach ; (2) the Quasi maximum Likelihood approach ; (3) a multi-steps recursive estimation approach (REC). We first run a Monte Carlo test which shows that the recursive method may be the most relevant approach for estimation purposes. We then turn to a sample of SP500 returns. We confirm that the REC estimates are statistically dominating the parameters estimated by the two other competing methods. Regardless of the selected model, REC estimates deliver the more stable results.Maximum likelihood method, related-GARCH process, recursive estimation method, mixture of Gaussian distribution, Generalized Hyperbolic distributions, SP500.

Option Pricing under GARCH models with Generalized Hyperbolic distribution (II) : Data and Results

In this paper, we provide a new dynamic asset pricing model for plain vanilla options and we discuss its ability to produce minimum mispricing errors on equity option books. The data set is the daily log returns of the French CAC40 index, on the period January 2, 1988, October 26, 2007. Under the historical measure, we adjust, on this data set, an EGARCH model with Generalized Hyperbolic innovations. We have shown (Chorro, Guégan and Ielpo, 2008) that when the pricing kernel is an exponential affine function of the state variables, the risk neutral distribution is unique and implies again a Generalized Hyperbolic dynamic, with changed parameters. Thus, using this theoretical result associated to Monte Carlo simulations, we compare our approach to natural competitors in order to test its efficiency. More generally, our empirical investigations analyze the ability of specific parametric innovations to reproduce market prices in the context of the exponential affine specification of the stochastic discount factor.Generalized Hyperbolic Distribution, Option pricing, Incomplete market, CAC40.

Martingalized Historical approach for Option Pricing

In a discrete time option pricing framework, we compare the empirical performance of two pricing methodologies, namely the affine stochastic discount factor (SDF) and the empirical martingale correction methodologies. Using a CAC 40 options dataset, the differences are found to be small: the higher order moment correction involved in the SDF approach may not be that essential to reduce option pricing errors. This paper puts into evidence the fact that an appropriate modelling under the historical measure associated with an adequate correction (that we call here a ”martingale correction”) permits to provide option prices which are close to market ones.Generalized Hyperbolic Distribution; Option pricing; Incomplete market; CAC40; Stochastic Discount Factor; Martingale Correction