diff options
Diffstat (limited to 'python')
| -rw-r--r-- | python/analytics/cms_spread.py | 23 |
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) |