The Reactive Volatility Model

We present a new volatility model, simple to implement, that includes a leverage effect whose return-volatility correlation function fits to empirical observations. This model is able to capture both the "retarded effect" induced by the specific risk, and the "panic effect", which occurs whenever systematic risk becomes the dominant factor. Consequently, in contrast to a GARCH model and a standard volatility estimate from the squared returns, this new model is as reactive as the implied volatility: the model adjusts itself in an instantaneous way to each variation of the single stock price or the stock index price and the adjustment is highly correlated to implied volatility changes. We also test the reactivity of our model using extreme events taken from the 470 most liquid European stocks over the last decade. We show that the reactive volatility model is more robust to extreme events, and it allows for the identification of precursors and replicas of extreme events

Is the Impact of ECB Monetary Policy on EMU Stock Market Returns asymmetric?

This paper investigates whether monetary policy has asymmetric effects on stock returns of the EUM countries at aggregate levels and, for six industry portfolios in France, Italy, Germany, Belgium and Netherlands respectively. In this work, a different measures of monetary policy innovation is adopted. The empirical results, in line with results from previous studies, indicate that for the EUM stock markets there is statistically significant relationship between policy innovations and stock markets returns. This finding is consistent with the hypothesis that positive monetary policy shock (e.g. contractionary policy) is an event that decrease future cash flow. Moreover, the finding from country size and industry portfolios indicate that monetary policy have larger asymmetric effect in industry portfolios of big countries (Italy, France and Germany) compared to the same industry portfolios of small countries (Netherlands and Belgium). However, the sign of the impact is for both groups the same. The policy implications of the analysis can be summarized as follows: if the ECB follows a contractionary monetary policy then the effect on the stock market returns will be lengthier and larger in bear markets. On the other hand, following the same policy, the effect of the ECB actions on the EMU stock markets returns will be smaller in bull markets. The results suggest that monetary policy is not neutral, at least in the short run and, moreover, that there is some role for anticipated ECB monetary policy to affect the stock market but that this role will also have asymmetric impacts on each single EMU country’s stock market.Monetary Policy, Markov-switching, Stock returns.

Volatility forecasting

Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3, 4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly. JEL Klassifikation: C10, C53, G1

Probability of informed trading and volatility for an ETF

We use the new procedure developed by Easley et al. to estimate the Probability of Informed Trading (PIN), based on the volume imbalance: Volume-Synchronized Probability of Informed Trading (VPIN). Unlike the previous method, this one does not require the use of numerical methods to estimate unobservable parameters. We also relate the VPIN metric to volatility measures. However, we use most efficient estimators of volatility which consider the number of jumps. Moreover, we add the VPIN to a Heterogeneous Autoregressive model of Realized Volatility to further investigate its relation with volatility. For the empirical analysis we use data on the exchange traded fund (SPY)

Semi-parametric estimation of joint large movements of risky assets

The classical approach to modelling the occurrence of joint large movements of asset returns is to assume multivariate normality for the distribution of asset returns. This implies independence between large returns. However, it is now recognised by both academics and practitioners that large movements of assets returns do not occur independently. This fact encourages the modelling joint large movements of asset returns as non-normal, a non trivial task mainly due to the natural scarcity of such extreme events. This paper shows how to estimate the probability of joint large movements of asset prices using a semi-parametric approach borrowed from extreme value theory (EVT). It helps to understand the contribution of individual assets to large portfolio losses in terms of joint large movements. The advantages of this approach are that it does not require the assumption of a specific parametric form for the dependence structure of the joint large movements, avoiding the model misspecification; it addresses specifically the scarcity of data which is a problem for the reliable fitting of fully parametric models; and it is applicable to portfolios of many assets: there is no dimension explosion. The paper includes an empirical analysis of international equity data showing how to implement semi-parametric EVT modelling and how to exploit its strengths to help understand the probability of joint large movements. We estimate the probability of joint large losses in a portfolio composed of the FTSE 100, Nikkei 250 and S&P 500 indices. Each of the index returns is found to be heavy tailed. The S&P 500 index has a much stronger effect on large portfolio losses than the FTSE 100, although having similar univariate tail heaviness

Smile from the Past: A general option pricing framework with multiple volatility and leverage components

In the current literature, the analytical tractability of discrete time option pricing models is guarantee only for rather specific type of models and pricing kernels. We propose a very general and fully analytical option pricing framework encompassing a wide class of discrete time models featuring multiple components structure in both volatility and leverage and a flexible pricing kernel with multiple risk premia. Although the proposed framework is general enough to include either GARCH-type volatility, Realized Volatility or a combination of the two, in this paper we focus on realized volatility option pricing models by extending the Heterogeneous Autoregressive Gamma (HARG) model of Corsi et al. (2012) to incorporate heterogeneous leverage structures with multiple components, while preserving closed-form solutions for option prices. Applying our analytically tractable asymmetric HARG model to a large sample of S&P 500 index options, we evidence its superior ability to price out-of-the-money options compared to existing benchmarks

Adverse selection costs, trading activity and price discovery in the NYSE: An empirical analysis

This paper studies the role that trading activity plays in the price discovery process of a NYSE-listed stock. We measure the expected information content of each trade by estimating its permanent price impact. It depends on observable trade features and market conditions. We also estimate the time required for quotes to incorporate all the information content of a particular trade. Our results show that price discovery is faster after risky trades and also at the extreme intervals of the session. The quote adjustment to trade-related shocks is progressive and this causes risk persistency and unusual short-term market conditions.Publicad

Price dynamics and trading volume: A semiparametric approach

In this paper we investigate the relation between price impact and trading volume for a sample of stocks listed on the New York Stock Exchange. The parametric VAR-models that have been used in the literature impose strong proportionality and symmetry restrictions on the price impact of trades, although market microstructure theory provides many reasons why these restrictions would not hold. We analyze a more flexible semiparametric partially linear specification and establish significant evidence for a nonlinear, asymmetric, increasing, and concave relation between trading volume and both immediate and persistent price impact. Moreover, we compare the price-impact functions obtained in the partially linear model to the ones generated by the parametric models and show that there are considerable differences. We test the parametric specifications against the partially linear model and show that the parametric models are rejected in favor of the semiparametric model. We also test the partially linear model against a more flexible fully nonparametric specification and show that this test does not reject the partially linear model

The adaptive nature of liquidity taking in limit order books

In financial markets, the order flow, defined as the process assuming value one for buy market orders and minus one for sell market orders, displays a very slowly decaying autocorrelation function. Since orders impact prices, reconciling the persistence of the order flow with market efficiency is a subtle issue. A possible solution is provided by asymmetric liquidity, which states that the impact of a buy or sell order is inversely related to the probability of its occurrence. We empirically find that when the order flow predictability increases in one direction, the liquidity in the opposite side decreases, but the probability that a trade moves the price decreases significantly. While the last mechanism is able to counterbalance the persistence of order flow and restore efficiency and diffusivity, the first acts in opposite direction. We introduce a statistical order book model where the persistence of the order flow is mitigated by adjusting the market order volume to the predictability of the order flow. The model reproduces the diffusive behaviour of prices at all time scales without fine-tuning the values of parameters, as well as the behaviour of most order book quantities as a function of the local predictability of order flow.Comment: 40 pages, 14 figures, and 2 tables; old figure 12 removed. Accepted for publication on JSTA

Volatility Forecasting

Volatility has been one of the most active and successful areas of research in time series econometrics and economic forecasting in recent decades. This chapter provides a selective survey of the most important theoretical developments and empirical insights to emerge from this burgeoning literature, with a distinct focus on forecasting applications. Volatility is inherently latent, and Section 1 begins with a brief intuitive account of various key volatility concepts. Section 2 then discusses a series of different economic situations in which volatility plays a crucial role, ranging from the use of volatility forecasts in portfolio allocation to density forecasting in risk management. Sections 3,4 and 5 present a variety of alternative procedures for univariate volatility modeling and forecasting based on the GARCH, stochastic volatility and realized volatility paradigms, respectively. Section 6 extends the discussion to the multivariate problem of forecasting conditional covariances and correlations, and Section 7 discusses volatility forecast evaluation methods in both univariate and multivariate cases. Section 8 concludes briefly.