It warrants emphasizing that our model does not assume there is a one-off investment outlay incurred immediately before installation of the capital project. We assume, instead, that operating cash flows and investment outlays accumulate over the entire term of the investment project. This means that the net cash flows from the project (by which we mean the operating cash flow less any investment outlays incurred in each period) might be negative, and so the present value of these cash flows can also be negative.

A white noise process (Hoel et al., 1972, p. 142) is the derivative of a Wiener L vy process (Hoel et al., 1972, p. 123). Furthermore, the coefficient associated with x ²( t) in the stochastic term of this formulation namely 2 r is chosen for computational and analytical convenience. By allowing d z( t) to be a white noise process with variance parameter ? ² not, in general, equal to unity, we can reduce the impact of this assumption.

For some alternative empirical evidence (and models) on this issue see the articles by Heston (1993) and Hull and White (1988).

A simple application of It 's lemma shows that the solution to this equation is:

where z( t) is a Wiener L vy process with unit variance parameter.

The Black and Scholes (1973) option valuation formula is likewise founded on a co-ordinate system which transforms the assumed geometric Brownian motion on which asset prices are based into a...