Add initial Quant.jl code for Black-Scholes

src/blackscholes.jl

@@ -0,0 +1,54 @@
+###
+# Black-Scholes model functionality for Julia.
+#
+# Designed to be a reference implementation of the Black-Scholes option
+# pricing formula, supporting the original formula and greeks calculation
+###
+using StatsFuns
+
+"""
+Calculate the value of $d_1$ in the Black-Scholes Formula
+"""
+d1 = function(σ, T, t, S, K, r)
+  return (σ .* sqrt(T-t)).^-1 * (log(S ./ K) + (r + σ.^2 / 2).*(T-t))
+end
+
+d1 = function(σ, T, S, K, r)
+  return d1(σ, T, 0, S, K, r)
+end
+
+d2 = function(d1_val, σ, T, t)
+  return d1_val - σ .* sqrt(T-t)
+end
+
+d2 = function(d1_val, σ, T)
+  return d2(d1_val, σ, T, 0)
+end
+
+blackscholes_call = function(σ, T, t, S, K, r)
+  d1_val = d1(σ, T, t, S, K, r)
+  d2_val = d2(d1_val, σ, T, t)
+
+  return normcdf(d1_val) .* S - normcdf(d2_val) .* K .* exp(-r .* (T - t))
+end
+
+blackscholes_call = function(σ, T, S, K, r)
+  d1_val = d1(σ, T, S, K, r)
+  d2_val = d2(d1_val, σ, T)
+
+  return normcdf(d1_val) .* S - normcdf(d2_val) .* K .* exp(-r .* T)
+end
+
+blackscholes_put = function(σ, T, t, S, K, r)
+  d1_val = d1(σ, T, t, S, K, r)
+  d2_val = d2(d1_val, σ, T, t)
+
+  return normcdf(-d2_val).*K.*exp(-r.*(T-t)) - normcdf(-d1).*S
+end
+
+blackscholes_put = function(σ, T, S, K, r)
+  d1_val = d1(σ, T, S, K, r)
+  d2_val = d2(d1_val, σ, T)
+
+  return normcdf(-d2_val).*K.*exp(-r.*T) - normcdf(-d1).*S
+end