Antonio Mele

SIGN- AND VOLATILITY-SWITCHING ARCH MODELS: THEORY AND APPLICATIONS TO INTERNATIONAL STOCK MARKETS

This paper develops two conditionally heteroscedastic models which allow an asymmetric reaction of the conditional volatility to the arrival of news. Such a reaction is induced by both the sign of past shocks and the size of past unexpected volatility. The proposed models are shown to converge in distribution to absolutely continuous Ito diffusion processes, as happens for other heteroscedastic formulations. One of the schemes developed in the paper--the Volatility-switching ARCH--differs from the existing asymmetric models insofar as it is able to capture a particular aspect of the behaviour of the volatilities, i.e., the reversion of their asymmetric reaction to news. Empirical evidence from stock market returns in six countries shows that such a model outperforms traditional asymmetric ARCH equations.

Modeling the changing asymmetry of conditional variances

Abstract We analyze the asymmetric response of the volatility to the arrival of shocks of opposite sign. After revising the major formulations developed so far to capture the phenomenon, a more general model is proposed; it cannot be rejected against three competing specifications when fitted to stock exchange indices returns.

Adding and subtracting Black-Scholes: A new approach to approximating derivative prices in continuous-time models

We develop a new approach to approximating asset prices in the context of continuous-time models. For any pricing model that lacks a closed-form solution, we provide a closed-form approximate solution, which relies on the expansion of the intractable model around an “auxiliary” one. We derive an expression for the difference between the true (but unknown) price and the auxiliary one, which we approximate in closed-form, and use to create increasingly improved refinements to the initial mispricing induced by the auxiliary model. The approach is intuitive, simple to implement, and leads to fast and extremely accurate approximations. We illustrate this method in a variety of contexts including option pricing with stochastic volatility, computation of Greeks, and the term structure of interest rates.

Volatility smiles and the information content of news

The paper investigates whether the impact of selected news - scheduled and un-scheduled - affects only the current conditional variance of financial prices or, by bringing new information to the market, induces also a revision of the implied variance, i.e. the variance expected to prevail over the life to maturity of an option. The latter phenomenon would signal that news is able to change permanently the consensus on the future economic environment. In addition to recent similar ana lyses which employ the at the money implied volatility to this aim, tests are also performed on the implied out of money and in the money volatilities. These are in fact extremely sensitive to lack of information about the future evolution of the price of the underlying asset: hence, their prices - as well as their implied volatilities - must change significantly after the occurrence of important events.

Approximating volatility diffusions with CEV-ARCH models

Aim of this article is to judge the empirical performance of Arch as diffusion approximations to models of the short-term rate with stochastic volatility and as filters of the unobserved volatility. We show that the estimation of the continuous time scheme to which a discrete time Arch model converges can be safely based on simple moment conditions linking the discrete time to the continuous time coefficients. A natural substitute of a global specification test for just-identified problems based on indirect inference shows in fact that this approximation to diffusions gives rise to a negligible disaggregation bias. Unlike previous literature in which standard Arch models approximated only specific diffusions, our estimation strategy relies on a new Arch model that approximates any CEV-diffusion model for the conditional volatility. A Monte-Carlo study reveals that the filtering performances of this model are remarkably good, even in the presence of an important kind of misspecification.

Asymmetries and non-linearities in economic activity

Industrial production is analysed for three countries. A GARCH framework is employed to model the conditional variances of the cycles, which are found to react asymmetrically to shocks of opposite sign; one of the three cases exhibits long-memory features. The ability of GARCH models at capturing all the heteroscedasticity of the data is tested against the null of deterministic chaos.

Adding and Subtracting Black-Scholes: A New Approach to Approximating Derivative Prices in Continuous Time Models

We develop a new approach to approximating asset prices in the context of continuous-time models. For any pricing model that lacks a closed-form solution, we provide a closed-form approximate solution, which relies on the expansion of the intractable model around an “auxiliary” one. We derive an expression for the difference between the true (but unknown) price and the auxiliary one, which we approximate in closed-form, and use to create increasingly improved refinements to the initial mispricing induced by the auxiliary model. The approach is intuitive, simple to implement, and leads to fast and extremely accurate approximations. We illustrate this method in a variety of contexts including option pricing with stochastic volatility, computation of Greeks, and the term structure of interest rates.

A stochastic variance model for absolute returns

Abstract Empirical research has shown that the autocorrelation function of a stationary series is maximised when the latter is raised to a positive power δ, which rarely coincides with two. Thus, both the GARCH and stochastic variance (SV) models fail to capture all the non-linear dependence of the data. The proposed model, in which δ equals one, improves the specification for the SV models.

The Price of Government Bond Volatility

Treasury price volatility comoves with equity volatility quite heterogeneously over time, with correlations ranging from negative to positive, and marked by periods of rapid movement. What is the price of Treasury volatility? How can we express this price in a model-free format? Despite the success of the CBOE equity VIX, no counterparts exist for US Treasuries and other government bond markets. Pricing Treasury price volatility in a model-free manner is a delicate issue for two reasons. First, volatility is referenced to an asset with finite maturity, a case where standard spanning arguments might fail to apply. Second, the markets we are interested in this paper obviously relate to contexts where interest rates are random, which requires tilting the basis assets we wish to price the volatility of. We develop contract designs for variance swaps applying to government bonds, and derive model-free indexes of government bond price expected volatility, based on the fair value of the contracts expressed in terms of option prices. We follow market practice and consider both percentage and basis point expected volatility. Basis point volatility can be priced in a model-free format even in the presence of jumps. We provide two algorithms to calculate the indexes through the use of American future options.

Volatility Indexes and Contracts for Eurodollar and Related Deposits

Eurodollar deposit volatility comoves with equity volatility quite heterogeneously over time, with correlations ranging from negative to positive, and marked by periods of rapid movement. What is the price of time deposit volatility? How can we express this price in a model-free format? Despite the success of the CBOE equity VIX, no counterparts exist for time deposits such as the Eurodollar. Pricing time deposit volatility in a model-free manner is a delicate issue because the contexts we are interested in are obviously those where interest rates are random, requiring tilting the basis assets we wish to price the volatility of. We develop contract designs for variance swaps applying to time deposits, and derive model-free indexes of time deposit expected volatility, based on the fair value of the contracts expressed in terms of option prices. We follow market practice and consider both percentage and basis point expected volatility. Basis point volatility can be priced in a model-free format even in the presence of jumps. We provide two algorithms to calculate the indexes through the use of American future options.