1 files changed, 34 insertions, 0 deletions
diff --git a/python/analytics/black.pyx b/python/analytics/black.pyx
new file mode 100644
index 00000000..80d13a1a
--- /dev/null
+++ b/python/analytics/black.pyx
@@ -0,0 +1,34 @@
+# cython: language_level=3, cdivision=True
+from libc.math cimport log, sqrt, erf
+from scipy.stats import norm
+import cython
+
+cpdef double cnd_erf(double d):
+    """ 2 * Phi where Phi is the cdf of a Normal """
+    cdef double RSQRT2 = 0.7071067811865475
+    return 1 + erf(RSQRT2 * d)
+
+
+cpdef double black(double F, double K, double T, double sigma, bint payer=True):
+    cdef:
+        double x = log(F / K)
+        double sigmaT = sigma * sqrt(T)
+        double d1 = (x + 0.5 * sigmaT * sigmaT) / sigmaT
+        double d2 = (x - 0.5 * sigmaT * sigmaT) / sigmaT
+    if payer:
+        return 0.5 * (F * cnd_erf(d1) - K * cnd_erf(d2))
+    else:
+        return 0.5 * (K * cnd_erf(-d2) - F * cnd_erf(-d1))
+
+
+cpdef double Nx(double F, double K, double sigma, double T):
+    return cnd_erf((log(F / K) - sigma ** 2 * T / 2) / (sigma * sqrt(T))) / 2
+
+
+cpdef double bachelier(double F, double K, double T, double sigma):
+    """ Bachelier formula for normal dynamics
+
+    need to multiply by discount factor
+    """
+    cdef double d1 = (F - K) / (sigma * sqrt(T))
+    return 0.5 * (F - K) * cnd_erf(d1) + sigma * sqrt(T) * norm.pdf(d1)