Add closed form Black-Scholes model

utils.go

@@ -0,0 +1,35 @@
+package main
+
+import "math"
+
+// NormCDF computes the Cumulative Density Function of a Standard Normal
+// Distribution.
+// Code adapted from https://www.johndcook.com/blog/cpp_phi/
+func NormCDF(z float64) float64 {
+	// constants
+	var a1, a2, a3, a4, a5, p, t, y, sign float64
+
+	a1 = 0.254829592
+	a2 = -0.284496736
+	a3 = 1.421413741
+	a4 = -1.453152027
+	a5 = 1.061405429
+	p = 0.3275911
+
+	sign = 1
+	if z < 0 {
+		sign = -1
+	}
+	x := math.Abs(z) / math.Sqrt2
+
+	t = 1.0 / (1.0 + p*x)
+	y = 1.0 - (((((a5*t+a4)*t)+a3)*t+a2)*t+a1)*t*math.Exp(-x*x)
+
+	return 0.5 * (1.0 + sign*y)
+}
+
+// NormPDF computes the Probability Density Function of a Standard Normal
+// Distribution.
+func NormPDF(z float64) float64 {
+	return 1 / math.Sqrt(2*math.Pi) * math.Exp(-math.Pow(z, 2)/2)
+}