The generalized lambda distribution applied to spot exchange rates

Many financial data series, such as spot currency exchange rates, exhibit heavy-tailed behavior. Traditional models, such as the Black-Scholes option pricing model, assume that the price of the underlying security follows a geometric Brownian motion process. Log-returns exhibiting heavy-tailed behavior cannot be captured by a geometric Brownian motion. Moreover, if a first order discretization scheme is applied to the price process, then the log-returns will be i.i.d. and normally distributed. Distributions such as the Student-t distributions, stable distributions with index alpha, and mixtures of normal distributions have been proposed to model log-returns of security prices exhibiting heavy-tailed behavior.; The generalized lambda distribution (GLD), a distribution that offers a wide range of skewness and kurtosis values and is able to closely approximate many of the commonly used statistical distributions, is a candidate for modeling the log-returns of security prices.; This thesis defines a multivariate generalized lambda distribution (MGLD) and uses it as a tool for modeling spot exchange rates. The MGLD not only fits the marginal distribution of each spot rate very well, but it is also able to capture the correlation structure of the spot rates for a set of currencies.; The volatility clustering behavior of log-returns can be included by considering MGARCH models with conditional distribution given by the MGLD. A hidden Markov model between two MGLDs is also considered as an alternative to model the non-i.i.d. structure of log-returns. An empirical study indicates that both the MGARCH(1,1) constant correlation model with MGLD noise and the hidden Markov model between two MGLDs fit the spot exchange rates series equally well.; A trading strategy for a multicurrency portfolio is considered by assuming the future log-monthly-returns of several spot rates follow the forward premium model. A simulation study indicates that the forward premium model with MGLD noise gives a better return than the corresponding model with Gaussian noise or the Student-t noise.