Computing a Multivariate Normal Integral for Valuing Compound Real Options

We extend the Geske (1979) model to a multivariate normal integral for the valuation of a compound real option. We compared the computing speeds and errors of three numerical integration methods, namely, Drezner's improved Gauss quadrature method, Monte Carlo method and Lattice method, together with appropriate critical value finding methods. It is found that secant method for finding critical values combined with Lattice method and run by Fortran took merely one second, Monte Carlo method 120 seconds. It is also found that the real option decreases with interest rate, not necessarily positively correlated with volatility , a result different from that anticipated under financial option theory. This is mainly because the underlying of real option is a non-traded asset, which brings dividend-like yield into the formula of compound real options. Dividend-like yield rises with the multiplication of correlation coefficient and . High indicates the poor diversification advantage of the new investment project in relation to the existing market portfolio, and the value of real call option decreases with . Conversely, when is low, the proposed project provides better diversification advantage and the real call option rises with . Irrespective of the value of , when interest rate increases, the value of real call option drops, especially when is high, the value of the project is dominated by interest rate.