Angelo Melino

Pricing foreign currency options with stochastic volatility

Abstract This paper investigates the consequences of stochastic volatility for pricing spot foreign currency options. A diffusion model for exchange rates with stochastic volatility is proposed and estimated. The parameter estimates are then used to price foreign currency options and the predictions are compared to observed market prices. We find that allowing volatility to be stochastic results in a much better fit to the empirical distribution of the Canada-U.S. exchange rate, and that this improvement in fit results in more accurate predictions of observed option prices.

Duration Dependence and Nonparametric Heterogeneity: A Monte Carlo Study

We examine the behaviour of the nonparametric maximum likelihood estimator (NPMLE) for a discrete duration model with unobserved heterogeneity and unknown duration dependence. We find that a nonparametric specification of either the duration dependence or unobserved heterogeneity, when the other feature of the hazard is known to be absent, leads to estimators that are well behaved even in modestly sized samples. In contrast, there is a large and systematic bias in the parameters of these components when both are specified nonparametrically, as well as a complementary bias in the coefficients on observed heterogeneity. Furthermore, these biases diminish very gradually as sample size increases. We find that a minor modification of the quasilikelihood that penalizes specifications with many points of support leads to a dramatic improvement.

Estimating the Continuous-Time Consumption-Based Asset-Pricing Model

The consumption-based asset-pricing model predicts that excess yields are determined by the markets degree of relative risk aversion and by the covariances of per capita consumption growth with asset returns. Estimation and testing are complicated by the fact that the models predictions relate to the instantaneous flow of consumption and point-in-time asset values, but only data on the integral or time average of the consumption flow are available. This article shows how to take account of the effects of time averaging on the covariances. We estimate the models parameters and test the overidentifying restrictions using six different data sets.

The Effects of Public Policy on Strike Duration

Hazard-function estimates are utilized to analyze the effect of numerous public policy variables on strike duration, based on 7,546 strikes in Canada between 1967 and 1985. We find that only the mandatory strike vote substantially reduced conditional duration. However, the policy variables generally had a more favorable effect on reducing strike incidence, so that on net they tended to reduce unconditional duration (incidence times conditional duration). Specifically, reduced unconditional duration was associated with the existence of conciliation and the requirement of a mandatory strike vote, but the prohibition on replacement workers had a perverse effect.

State Dependent Preferences Can Explain the Equity Premium Puzzle

We introduce state dependent recursive preferences into the Mehra-Prescott economy. We show that such preferences can match the historical first two moments of the returns on equity and the risk free rate. Other authors have reported similar results using state dependent expected utility preferences. These authors have tended to emphasize the importance of countercyclical risk aversion in explaining the equity premium puzzle. We find that countercyclical risk aversion plays an important role but only when combined with modest cyclical variation in intertemporal substitution.

Testing for Sample Selection Bias

A simple regression test of the null hypothesis of no sample selection bias has been suggested by J. J. Heckman. Because of its computational simplicity, this test is widely used by applied researchers. This paper shows that Heckmans test is equivalent to the Lagrange multiplier test of the null hypothesis. This allows us to readily deduce that the simple regression test also has desirable large sample properties.

The pricing of foreign currency options

This study examines the assumption that the exchange rate follows a log-normal probability distribution and it tests whether different stochastic specifications translate into important differences in implied option prices. The authors investigate a class of processes, which includes the log-normal probability distribution as a limiting case. None of the models perform particularly well. The main problem appears to be that the volatility estimates from actual exchange rate data are significantly smaller than those implied by observed option prices.

Misspecification and the pricing and hedging of long-term foreign currency options

Abstract This study examines the effects of stochastic volatility upon the pricing and hedging of long-term foreign currency options. The traditional method of pricing such options uses a constant volatility option model with an implicit volatility derived from a short-term traded option. We show that the traditional method leads to small pricing errors for short- and medium-term options, but does a poor job in pricing long-term options. The traditional method also does a poor job for all maturities in determining the derivatives of the options value with respect to the exchange rate (delta) and the volatility (vega). The errors in calculating these derivatives, which are used in forming the replicating portfolio, lead to large and costly errors in error hedging.

A Note on the Interpretation of Regression Coefficients within a Class of Truncated Distributions

DESPITE THE INTENSE ACTIVITY in the area of estimation of limited dependent variable (LDV) models (see, for example, the Fall 1976 issue of the Annals of Economic and Social Measurement), the interpretation of regression coefficients in truncated regression models has been largely ignored. This issue should not be taken lightly since the obvious interpretation which equates regression coefficients to partial derivatives of the conditional mean of the dependent variable is unfortunately incorrect. One specific implication of the results presented here is that whenever the dependent variable y in the usual classical linear normal regression model is truncated above and/or below, then the effect of the fth regressor on the conditional mean of y is proportional to, but not equal to, the fth regression coefficient. However, more generally this note presents a simple expression for the effect of the fth regressor on any conditional moment of y in terms of a generalized LDV model introduced by Poirier [3]. Poirier introduced a general LDV model which permitted skewness in a pre-truncated variable by transforming it within the class of transformations suggested by Box and Cox

The response of interest rates to the Federal Reserve's weekly money announcements: The 'puzzle' of anticipated money

Researchers, using the survey conducted by Money Market Services, Inc., have found that the anticipated component in the Federal Reserves weekly money supply announcement is negatively correlated with the post- announcement change in market yields. We prove that eliminating a (downward) bias in the measure of anticipated money can, in theory, eliminate this puzzle, but that improving the efficiency of an already unbiased measure cannot. We find, using Canadian as well as U.S. interest rate data, that correcting the downward bias in the survey measure reduces, but does not eliminate, the role of anticipated money.