Add initial Quant.jl code for Black-Scholes

src/Quant.jl

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+
+"""
+Quantitative Finance methods for Julia
+
+Designed to implement many helpful methods that are often repeated; we don't
+want seventeen different versions of the Black-Scholes equation floating
+around, and re-writing a Geometric Brownian Motion simulation for every
+new project is just tedious.
+"""
+module Quant.jl
+
+export
+
+  # Black-Scholes functionality
+  d1,
+  d2,
+  blackscholes_call,
+  blackscholes_put,
+
+include("blackscholes.jl")
+
+end

src/blackscholes.jl

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+###
+# 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

test/blackscholes.jl

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+using Quant
+
+@test_approx blackscholes_call(.25, 2, 1, 100, 95, .05) 15.047
+
+@test_approx blackscholes_call(.25, 1, 100, 95, .05) blackscholes_call(.25, 2, 1, 100, 95, .05)

test/runtests.jl

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+include("blackscholes.jl")