Journal of Computational Finance, 1 (4) (1998), 5–10.
An infinite series expansion is given for the bivariate normal cumulative distribution function. This expansion converges as a series of powers of , where ρ is the correlation coefficient, and thus represents a good alternative to the tetrachoric series when ρ is large in absolute value.
The cumulative normal distribution function
appears frequently in modern finance: Essentially all explicit equations of options pricing, starting with the Black-Scholes formula, involve this function in one form or another. Increasingly, however, there is also a need for the bivariate cumulative normal distribution function
where the bivariate normal density is given by
This need arises in at least the following areas: