1 files changed, 23 insertions, 0 deletions
diff --git a/python/analytics/cms_spread.py b/python/analytics/cms_spread.py
new file mode 100644
index 00000000..10a23417
--- /dev/null
+++ b/python/analytics/cms_spread.py
@@ -0,0 +1,23 @@
+from .tranche_functions import GHquad
+from math import exp, sqrt, log
+from .blac import cnd_erf
+
+def CMS_spread(T_alpha, X, beta, gamma):
+    Z, w = GHquad(100)
+    return np.inner(f(Z), w)
+
+def f(v, X, S_alpha_beta, S_alpha_gamma, mu_beta, mu_gamma, T_alpha, rho):
+    h = h(v, X, S_alpha_beta, mu_beta, sigma_alpha_beta, T_alpha)
+    u = rho * sigma_alpha_gamma * sqrt(T_alpha) * v
+    d = sigma_alpha_gamma * sqrt(T_alpha) * sqrt(1 - rho ** 2)
+    r = mu_gamma * T_alpha - 0.5 * rho * rho * sigma_alpha_gamma ** 2 * T_alpha + u
+    u0 = log(S_alpha_gamma / h) + u
+    u1 = u0 + (mu_gamma + (0.5 - rho ** 2) * sigma_alpha_gamma**2) * T_alpha
+    u2 = u0 + (mu_gamma - 0.5 * sigma_alpha_gamma**2) * T_alpha
+    return 0.5 * (S_alpha_gamma * exp(r) * cnd_erf(u1 / d) - h * cnd_erf(u2 / d))
+
+
+def h(v, X, S_alpha_beta, mu_beta, sigma_alpha_beta, T_alpha):
+    r = (mu_beta - 0.5 * sigma_alpha_beta * sigma_alpha_beta) * T_alpha + \
+        sigma_alpha_beta * sqrt(T_alpha) * v
+    return X + S_alpha_beta * exp(r)