Antonio Roma

Stochastic Volatility Option Pricing

This paper examines alternative methods for pricing options when the underlying security volatility is stochastic. We show that when there is no correlation between innovations in security price and volatility, the characteristic function of the average variance of the price process plays a pivotal role. It may be used to simplify Fourier option pricing techniques and to implement simple power series methods. We compare these methods for the alternative mean-reverting stochastic volatility models introduced by Stein and Stein (1991) and Heston (1993). We also examine the biases in the Black-Scholes model that are eliminated by allowing for stochastic volatility, and we correct some errors in the Stein and Stein (1991) analysis of this issue.

A jump diffusion model for the European monetary system

Abstract We propose a general continuous time bivariate jump-diffusion representation for the exchange rates of European currencies. Our model captures key features of the exchange rate mechanism. Fluctuation within bilateral limits is modeled by appropriate diffusion dynamics, while discontinuous variation in the level of the fluctuation band is posited to have a jump structure. Under specific assumptions, the probability distribution of the exchange rate process is derived analytically. We also perform an empirical investigation of these exchange rates. Comparing the fit of alternative models, we find some evidence of mean reversion inside the bands for these exchange rates. (JEL F33, C51).

Target zone modelling and estimation for European Monetary System exchange rates

Abstract Krugman (1991) provided a rigorous economic argument for the merits of target zone exchange rate arrangements. His analysis revealed the existence of a stabilizing nonlinear relation between the exchange rate and its driving fundamentals. However, the econometric testing of this relationship has proved difficult. We use data from the European Monetary System (EMS) to implement efficient testing of the Krugman model and extensions which allow mean reversion in the fundamentals process. In particular, we model the fundamentals driving the bilateral exchange rates of participating currencies by means of an Ornstein Uhlenbeck process with reflecting barriers. This specification captures the enforcement of an exchange rate fluctuation band through central bank intervention at band limits as well as through intramarginal intervention. Our empirical work is based on a period of exceptional stability in exchange rate markets and well approximates the credible band limit assumptions common in the target zone modelling literature. Building on recent work by Ricciardi and Sacerdote (1987), de Jong (1991), and Lindberg and Soderlind (1991, 1992), we implement full maximum likelihood estimation of the parameters of the time series dynamics for the most heavily traded bilateral exchange rates in the EMS. In doing so we identify the functional relation between the fundamentals and the exchange rate and quantify the nonlinearity in this relation. When nonlinearity is not present, a restriction of the model posits that the exchange rate, per se, follows a reflected OU process. A further restriction contains reflected Brownian motion as a nested special case. Our analysis affords a description of the alternative exchange rate policies adopted in the various countries party to the EMS.

Detecting mean reversion within reflecting barriers: application to the European Exchange Rate Mechanism

This paper derives a statistical test, based on the first-order autocorrelation, to ascertain whether a stochastic process evolving within reflecting barriers is mean reverting. Under these conditions the standard unit root analysis does not apply. Since the presence of reflecting barriers per se will induce mean reverting behaviour, the detection of mean reversion inside the two boundaries requires that the effect of reflection be properly accounted for. This statistical procedure may be useful in a number of economic applications which involve an assesment on the dynamics of bounded variables: e.g. the estimation of the mean reversion of ratios in capital structure theory, market share analysis, or the empirical testing of target zones models for exchange rates. We exemplify the inappropriateness of standard unit root analysis in these situations using European Monetary System exchange rate data. Our methodology is helpful in deciding whether the mean reverting behaviour of these exchange rates is due solely to local behaviour at the barriers, or whether a more complex interpretation is warranted. We apply our test to the target zone model introduced by Krugman where the intervention bands are credible. We study bilateral exchange rates of currencies party to the European Monetary System during a period of sustained stability consistent with the credible band assumption. Our results are consistent with those obtained employing significantly more complex maximum likelihood procedures.

A Comparison of Alternative Non-Parametric Estimators of the Short Rate Diffusion Coefficient

In this paper we discuss the estimation of the diffusion coefficient of one-factor models for the short rate via non-parametric methods. We test the estimators proposed by Ait Sahalia (1996a), Stanton (1997) and Bandi and Phillips (2003) on Monte Carlo simulation of the Vasicek and CIR model and show that all estimators, especially that proposed by Ait-Sahalia (1996a), are problematic for values of the mean reversion coefficient typically displayed by interest rate data. Moreover all estimators depend crucially on the choice of the bandwith parameter. Data analysis shows that the estimators lead to different estimates on the data set analyzed by Ait-Sahalia (1996a) and Stanton (1997); moreover we show that the two data set are inherently different.

Energy, money, and pollution

This paper explores general equilibrium consumption choices and interest rate determination in a two-period model in which the production side explicitly describes the thermodynamic process unavoidably connected with production, as argued by Georgescu Roegen. A simple energy based production process is modeled, which is not in a stationary state. The resulting production function is time dependent. In neoclassical general equilibrium the thermodynamic implication of the production process, i.e. the production of waste, will not be taken into account by decision making agents. For welfare optimality, the resulting externality need be corrected by a social planner,or through the use of environmental related taxation. However, it is shown that imposing in the same economy energy as a medium of exchange (money), makes agents energy conscious and decreases the externality associated with entropic waste production through a market mechanism, without the need for the intervention. In the limit case in which production occurs in thermodynamic equilibrium, no entropic waste is produced, and the model collapses to the nested neoclassical model. A contribution of the proposed approach is the determination of energy (money) prices in general equilibrium. Despite the fact that energy does not enter the agents utility function, and therefore has no direct value, money prices and interest rate can be fully characterized in the model due precisely to the production technology adopted. The change in the numeraire and medium of exchange performed affects the economy due to the non stationarity of the production process, but has no effect in the limit case in which the productive process reaches steady state.