Normal

Standard-normal density, distribution and quantile — the numerics the analytic pricer oracles in this package share.

cdf is West's rational approximation (double precision, absolute error below 1e-15), not the lighter erfc approximation in BlackScholes — the oracle Greeks in this package are taken by central differencing the closed forms, and a second difference amplifies any bias in N(x) by 1/h^2. inverseCdf is the Acklam rational approximation refined by one Halley step against that cdf, used where a formula needs Phi^{-1} — the Bachelier implied strike, the Gaussian-copula default threshold.

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Methods

static double pdf(double x)

Standard-normal probability density.

static double cdf(double x)

Standard-normal cumulative distribution, West's algorithm ("Better approximations to cumulative normal functions", 2005): a seven-term rational for |x| < 7.07 and a continued fraction beyond it.

static double inverseCdf(double p)

Standard-normal quantile Phi^{-1}(p) for p in (0, 1). Acklam's rational approximation with one Halley refinement against cdf.