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Diffstat (limited to 'python/analytics/black.py')
| -rw-r--r-- | python/analytics/black.py | 52 |
1 files changed, 0 insertions, 52 deletions
diff --git a/python/analytics/black.py b/python/analytics/black.py deleted file mode 100644 index 781732d9..00000000 --- a/python/analytics/black.py +++ /dev/null @@ -1,52 +0,0 @@ -from math import log, sqrt, erf -from numba import jit, float64, boolean -from scipy.stats import norm -import math - - -def d1(F, K, sigma, T): - return (log(F / K) + sigma ** 2 * T / 2) / (sigma * math.sqrt(T)) - - -def d2(F, K, sigma, T): - return d1(F, K, sigma, T) - sigma * math.sqrt(T) - - -@jit(cache=True, nopython=True) -def d12(F, K, sigma, T): - sigmaT = sigma * sqrt(T) - d1 = log(F / K) / sigmaT - d2 = d1 - d1 += 0.5 * sigmaT - d2 -= 0.5 * sigmaT - return d1, d2 - - -@jit(float64(float64), cache=True, nopython=True) -def cnd_erf(d): - """ 2 * Phi where Phi is the cdf of a Normal """ - RSQRT2 = 0.7071067811865475 - return 1 + erf(RSQRT2 * d) - - -@jit(float64(float64, float64, float64, float64, boolean), cache=True, nopython=True) -def black(F, K, T, sigma, payer=True): - d1, d2 = d12(F, K, sigma, T) - 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)) - - -@jit(float64(float64, float64, float64, float64), cache=True, nopython=True) -def Nx(F, K, sigma, T): - return cnd_erf((log(F / K) - sigma ** 2 * T / 2) / (sigma * sqrt(T))) / 2 - - -def bachelier(F, K, T, sigma): - """ Bachelier formula for normal dynamics - - need to multiply by discount factor - """ - d1 = (F - K) / (sigma * sqrt(T)) - return 0.5 * (F - K) * cnd_erf(d1) + sigma * sqrt(T) * norm.pdf(d1) |
