From e9d24adbfd21477e918fcc33a0a6028325dbe72b Mon Sep 17 00:00:00 2001
From: bspeice <bspeice.nc@gmail.com>
Date: Sat, 5 Mar 2016 18:50:53 -0500
Subject: [PATCH] Handle array inputs to black scholes

---
 REQUIRE              |  2 +-
 src/blackscholes.jl  |  8 +++++---
 test/blackscholes.jl | 15 ++++++++++++++-
 3 files changed, 20 insertions(+), 5 deletions(-)

diff --git a/REQUIRE b/REQUIRE
index 7960486..48285cb 100644
--- a/REQUIRE
+++ b/REQUIRE
@@ -1 +1 @@
-StatsFuns
+using Distributions
diff --git a/src/blackscholes.jl b/src/blackscholes.jl
index e056b86..2c44feb 100644
--- a/src/blackscholes.jl
+++ b/src/blackscholes.jl
@@ -4,7 +4,9 @@
 # Designed to be a reference implementation of the Black-Scholes option
 # pricing formula, supporting the original formula and greeks calculation
 ###
-using StatsFuns
+using Distributions
+
+Φ = x -> cdf(Normal(0, 1), x)
 
 """
 Calculate the value of \$d_1\$ in the Black-Scholes Formula
@@ -21,12 +23,12 @@ function blackscholes_call(S, K, σ, r, T, t=0)
   d1_val = d1(S, K, σ, r, T, t)
   d2_val = d2(d1_val, σ, T, t)
 
-  return normcdf(d1_val) .* S - normcdf(d2_val) .* K .* exp(-r .* (T - t))
+  return Φ(d1_val) .* S - Φ(d2_val) .* K .* exp(-r .* (T - t))
 end
 
 function blackscholes_put(S, K, σ, r, T, t=0)
   d1_val = d1(S, K, σ, r, T, t)
   d2_val = d2(d1_val, σ, T, t)
 
-  return normcdf(-d2_val).*K.*exp(-r.*(T-t)) - normcdf(-d1_val).*S
+  return Φ(-d2_val).*K.*exp(-r.*(T-t)) - Φ(-d1_val).*S
 end
diff --git a/test/blackscholes.jl b/test/blackscholes.jl
index 935fea9..52f4f87 100644
--- a/test/blackscholes.jl
+++ b/test/blackscholes.jl
@@ -3,7 +3,20 @@ using Base.Test
 using Quant
 
 @test 15.047 < blackscholes_call(100, 95, .25, .05, 2, 1) < 15.0471
-@test blackscholes_call(100, 95, .25, .05, 2, 1) == blackscholes_call(100, 95, .25, .05, 1)
+@test blackscholes_call(100, 95, .25, .05, 2, 1) ==
+  blackscholes_call(100, 95, .25, .05, 1)
+
+precompute_low = [15.047, 15.047]
+precompute_high = [15.0471, 15.0471]
+S = [100, 100]; K = [95, 95]; σ = [.25, .25]; r = [.05, .05]
+T = [2, 2]; t = [1, 1]
+@test all(precompute_low .< blackscholes_call(S, K, σ, r, T, t)
+  .< precompute_high)
 
 @test 5.413 < blackscholes_put(100, 95, .25, .05, 2, 1) < 5.414
 @test blackscholes_put(100, 95, .25, .05, 2, 1) == blackscholes_put(100, 95, .25, .05, 1)
+
+precompute_low = [5.413, 5.413]
+precompute_high = [5.414, 5.414]
+@test all(precompute_low .< blackscholes_put(S, K, σ, r, T, t)
+  .< precompute_high)