cbnd

3 באוק׳ 2022

Library "cbnd"

Description:
A standalone Cumulative Bivariate Normal Distribution (CBND) functions that do not require any external libraries.
This includes 3 different CBND calculations: Drezner(1978), Drezner and Wesolowsky (1990), and Genz (2004)

Comments:
The standardized cumulative normal distribution function returns the probability that one random
variable is less than a and that a second random variable is less than b when the correlation
between the two variables is p. Since no closed-form solution exists for the bivariate cumulative
normal distribution, we present three approximations. The first one is the well-known
Drezner (1978) algorithm. The second one is the more efficient Drezner and Wesolowsky (1990)
algorithm. The third is the Genz (2004) algorithm, which is the most accurate one and therefore
our recommended algorithm. West (2005b) and Agca and Chance (2003) discuss the speed and
accuracy of bivariate normal distribution approximations for use in option pricing in
ore detail.

Reference:
The Complete Guide to Option Pricing Formulas, 2nd ed. (Espen Gaarder Haug)

CBND1(A, b, rho)
  Returns the Cumulative Bivariate Normal Distribution (CBND) using Drezner 1978 Algorithm
  Parameters:
    A: float,
    b: float,
    rho: float,
  Returns: float.

CBND2(A, b, rho)
  Returns the Cumulative Bivariate Normal Distribution (CBND) using Drezner and Wesolowsky (1990) function
  Parameters:
    A: float,
    b: float,
    rho: float,
  Returns: float.

CBND3(x, y, rho)
  Returns the Cumulative Bivariate Normal Distribution (CBND) using Genz (2004) algorithm (this is the preferred method)
  Parameters:
    x: float,
    y: float,
    rho: float,
  Returns: float.