A multivariate invariance principle is given for dependent processes exhibiting trending variances and other types of global nonstationarity. The limit processes obtained in these results are not Brownian motion, but members of a related class of Gaussian diffusion processes. Also derived is the...

The Black and Scholes option pricing formula is shown to be a good approximation for valuing options when stock returns are assumed to follow a poisson driven lognormal jump process posited by Merton. Empirical results are given for options on Australian and U.S. stocks.