On the relevance of modeling volatility for pricing purposes

This paper presents a two-factor (Vasicek-CIR) model of the term structure of interest rates and develops its pricing and empirical properties. We assume that default free discount bond prices are determined by the time to maturity and two factors, the long-term interest rate and the spread. Assuming a certain process for both factors, a general bond pricing equation is derived and a closed-form expression for bond prices is obtained. Empirical evidence of the model's performance in comparisson with a double Vasicek model is presented. The main conclusion is that the modeling of the volatility in the long-term rate process can help (in a large amount) to fit the observed data can improve - in a reasonable quantity - the prediction of the future movements in the medium- and long-term interest rates. However, for shorter maturities, it is shown that the pricing errors are, basically, negligible and it is not so clear which is the best model to be used.

Local volatility changes in the black-scholes model

In this paper we address a problem arising in risk management; namely the study of price variations of different contingent claims in the Black-Scholes model due to anticipating future events. The method we propose to use is an extension of the classical Vega index, i.e. the price derivative with respect to the constant volatility, in thesense that we perturb the volatility in different directions. Thisdirectional derivative, which we denote the local Vega index, will serve as the main object in the paper and one of the purposes is to relate it to the classical Vega index. We show that for all contingent claims studied in this paper the local Vega index can be expressed as a weighted average of the perturbation in volatility. In the particular case where the interest rate and the volatility are constant and the perturbation is deterministic, the local Vega index is an average of this perturbation multiplied by the classical Vega index. We also study the well-known goal problem of maximizing the probability of a perfect hedge and show that the speed of convergence is in fact dependent of the local Vega index.

A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

Monetary policy and exchange rate volatility in a small open economy

We lay out a small open economy version of the Calvo sticky price model, and show how the equilibrium dynamics can be reduced to simple representation in domestic inflation and the output gap. We use the resulting framework to analyze the macroeconomic implications of three alternative rule-based policy regimes for the small open economy: domestic inflation and CPI-based Taylor rules, and an exchange rate peg. We show that a key difference amongthese regimes lies in the relative amount of exchange rate volatility that they entail. We also discuss a special case for which domestic inflation targeting constitutes the optimal policy, and where a simple second order approximation to the utility of the representative consumer can be derived and used to evaluate the welfare losses associated with the suboptimal rules.

On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

A note on the Malliavin differentiability of the Heston volatility

We show that the Heston volatility or equivalently the Cox-Ingersoll-Ross process is Malliavin differentiable and give an explicit expression for the derivative. This result assures the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model and the Cox-Ingersoll-Ross model for interest rates.

The great diversification and its undoing

We investigate the hypothesis that macroeconomic fluctuations are primitively theresults of many microeconomic shocks, and show that it has significant explanatorypower for the evolution of macroeconomic volatility. We define ?fundamental? volatilityas the volatility that would arise from an economy made entirely of idiosyncratic microeconomicshocks, occurring primitively at the level of sectors or firms. In its empiricalconstruction, motivated by a simple model, the sales share of different sectors vary overtime (in a way we directly measure), while the volatility of those sectors remains constant.We find that fundamental volatility accounts for the swings in macroeconomicvolatility in the US and the other major world economies in the past half century. Itaccounts for the ?great moderation? and its undoing. Controlling for our measure offundamental volatility, there is no break in output volatility. The initial great moderationis due to a decreasing share of manufacturing between 1975 and 1985. The recentrise of macroeconomic volatility is due to the increase of the size of the financial sector.We provide a model to think quantitatively about the large comovement generated byidiosyncratic shocks. As the origin of aggregate shocks can be traced to identifiablemicroeconomic shocks, we may better understand the origins of aggregate fluctuations.

Extreme times for volatility processes

Extreme times techniques, generally applied to nonequilibrium statistical mechanical processes, are also useful for a better understanding of financial markets. We present a detailed study on the mean first-passage time for the volatility of return time series. The empirical results extracted from daily data of major indices seem to follow the same law regardless of the kind of index thus suggesting an universal pattern. The empirical mean first-passage time to a certain level L is fairly different from that of the Wiener process showing a dissimilar behavior depending on whether L is higher or lower than the average volatility. All of this indicates a more complex dynamics in which a reverting force drives volatility toward its mean value. We thus present the mean first-passage time expressions of the most common stochastic volatility models whose approach is comparable to the random diffusion description. We discuss asymptotic approximations of these models and confront them to empirical results with a good agreement with the exponential Ornstein-Uhlenbeck model.

Firms, destinations, and aggregate fluctuations

This paper uses a database covering the universe of French firms for the period 1990-2007 to provide a forensic account of the role of individual firms in generating aggregatefluctuations. We set up a simple multi-sector model of heterogeneous firms selling tomultiple markets to motivate a theoretically-founded decomposition of firms' annualsales growth rate into different components. We find that the firm-specific componentcontributes substantially to aggregate sales volatility, mattering about as much as thecomponents capturing shocks that are common across firms within a sector or country.We then decompose the firm-specific component to provide evidence on two mechanismsthat generate aggregate fluctuations from microeconomic shocks highlighted in the recentliterature: (i) when the firm size distribution is fat-tailed, idiosyncratic shocks tolarge firms directly contribute to aggregate fluctuations; and (ii) aggregate fluctuationscan arise from idiosyncratic shocks due to input-output linkages across the economy.Firm linkages are approximately three times as important as the direct effect of firmshocks in driving aggregate fluctuations.

How Do Aggregate Fluctuations Depend on the Network Structure of the Economy?

[spa] En este artículo, analizamos la volatilidad agregada de una economía estilizada donde los agentes estann conectados en redes. Si hay relaciones estratégicas entre las acciones de los agentes, choques idiosincráticos pueden generar fluctuaciones agregadas. Demonstramos que la volatilidad agregada depende de la estructura de redes de la economía de dos maneras. Por un lado, si hay más conexiones en la economía en su conjunto, la volatilidad agregada es más baja. Por otro lado, si las conexiones están más concentradas, la volatilidad agregada es más alta. Presentamos una aplicación de nuestras predicciones teóricas que utiliza datos de EEUU de conexiones intrasectoriales y de diversificación de las empresas.

How Do Aggregate Fluctuations Depend on the Network Structure of the Economy?

[spa] En este artículo, analizamos la volatilidad agregada de una economía estilizada donde los agentes estann conectados en redes. Si hay relaciones estratégicas entre las acciones de los agentes, choques idiosincráticos pueden generar fluctuaciones agregadas. Demonstramos que la volatilidad agregada depende de la estructura de redes de la economía de dos maneras. Por un lado, si hay más conexiones en la economía en su conjunto, la volatilidad agregada es más baja. Por otro lado, si las conexiones están más concentradas, la volatilidad agregada es más alta. Presentamos una aplicación de nuestras predicciones teóricas que utiliza datos de EEUU de conexiones intrasectoriales y de diversificación de las empresas.

Financial stress transmission in EMU sovereign bond market volatility: a connectedness analysis

This paper measures the connectedness in EMU sovereign market volatility between April 1999 and January 2014, in order to monitor stress transmission and to identify episodes of intensive spillovers from one country to the others. To this end, we first perform a static and dynamic analysis to measure the total volatility connectedness in the entire period (the system-wide approach) using a framework recently proposed by Diebold and Yılmaz (2014). Second, we make use of a dynamic analysis to evaluate the net directional connectedness for each country and apply panel model techniques to investigate its determinants. Finally, to gain further insights, we examine the timevarying behaviour of net pair-wise directional connectedness at different stages of the recent sovereign debt crisis.

Volatility spillovers in EMU sovereign bond markets

We analyse volatility spillovers in EMU sovereign bond markets. First, we examine the unconditional patterns during the full sample (April 1999-January 2014) using a measure recently proposed by Diebold and Yılmaz (2012). Second, we make use of a dynamic analysis to evaluate net directional volatility spillovers for each of the eleven countries under study, and to determine whether core and peripheral markets present differences. Finally, we apply a panel analysis to empirically investigate the determinants of net directional spillovers of this kind.

Security prices and market transparency: the role of prior information

This paper analyzes the role of traders' priors (proper versus improper) on the implications of market transparency by comparing a pre-trade transparent market with an opaque market in a set-up based on Madhavan (1996). We show that prices may be more informative in the opaque market, regardless of how priors are modelled. In contrast, the comparison of market liquidity and volatility in the two market structures are affected by prior specification. Key words: Market microstructure, Transparency, Prior information