# Speed and accuracy comparison of bivariate normal distribution approximations for option pricing

## Senay Agca, Don M. Chance

#### Abstract

ABSTRACT

Pricing compound and min–max options requires approximation of the bivariate normal probability. We compare the performance of five analytical approximation methods for bivariate normal probabilities used in the computation of compound and min–max options against an externally tested benchmark of Simpson numerical integration. Each of the methods is very accurate with all probability errors less than 10–6 and the average probability error less than 10–7. The maximum error in an option price calculation is US$0.01, the average error is less than 2.0 × 10–4, and an error of as large as US$0.01 is rare. The Divgi method is the most accurate method for compound options, and the Owen method is the most accurate for min–max options. The Drezner–Wesolowsky method performs well in terms of accuracy and best in terms of speed. No single method emerges as the best overall, though the more widely cited Drezner method is consistently the least accurate, as well as the second slowest method.