diff options
Diffstat (limited to 'python/analytics/sabr.py')
| -rw-r--r-- | python/analytics/sabr.py | 140 |
1 files changed, 0 insertions, 140 deletions
diff --git a/python/analytics/sabr.py b/python/analytics/sabr.py deleted file mode 100644 index 71b42cad..00000000 --- a/python/analytics/sabr.py +++ /dev/null @@ -1,140 +0,0 @@ -import datetime
-import math
-import numpy as np
-
-
-def sabr_lognormal(alpha, rho, nu, F, K, T):
- A = 1 + (0.25 * (alpha * nu * rho) + nu * nu * (2 - 3 * rho * rho) / 24.0) * T
- if F == K:
- VOL = alpha * A
- elif F != K:
- nulogFK = nu * math.log(F / K)
- z = nulogFK / alpha
- x = math.log((math.sqrt(1 - 2 * rho * z + z ** 2) + z - rho) / (1 - rho))
- VOL = (nulogFK * A) / x
- return VOL
-
-
-def sabr_normal(alpha, rho, nu, F, K, T):
- if F == K:
- V = F
- A = (
- 1
- + (alpha * alpha / (24.0 * V * V) + nu * nu * (2 - 3 * rho * rho) / 24.0)
- * T
- )
- VOL = (alpha / V) * A
- elif F != K:
- V = math.sqrt(F * K)
- logFK = math.log(F / K)
- z = (nu / alpha) * V * logFK
- x = math.log((math.sqrt(1 - 2 * rho * z + z ** 2) + z - rho) / (1 - rho))
- A = (
- 1
- + (
- (alpha * alpha) / (24.0 * (V * V))
- + ((nu * nu) * (2 - 3 * (rho * rho)) / 24.0)
- )
- * T
- )
- logFK2 = logFK * logFK
- B = 1 / 1920.0 * logFK2 + 1 / 24.0
- B = 1 + B * logFK2
- VOL = (nu * logFK * A) / (x * B)
- return VOL
-
-
-def sabr(alpha, beta, rho, nu, F, K, T):
- if beta == 0.0:
- return sabr_normal(alpha, rho, nu, F, K, T)
- elif beta == 1.0:
- return sabr_lognormal(alpha, rho, nu, F, K, T)
- else:
- if F == K: # ATM formula
- V = F ** (1 - beta)
- A = (
- 1
- + (
- ((1 - beta) ** 2 * alpha ** 2) / (24.0 * (V ** 2))
- + (alpha * beta * nu * rho) / (4.0 * V)
- + ((nu ** 2) * (2 - 3 * (rho ** 2)) / 24.0)
- )
- * T
- )
- VOL = (alpha / V) * A
- elif F != K: # not-ATM formula
- V = (F * K) ** ((1 - beta) / 2.0)
- logFK = math.log(F / K)
- z = (nu / alpha) * V * logFK
- x = math.log((math.sqrt(1 - 2 * rho * z + z ** 2) + z - rho) / (1 - rho))
- A = (
- 1
- + (
- ((1 - beta) ** 2 * alpha ** 2) / (24.0 * (V ** 2))
- + (alpha * beta * nu * rho) / (4.0 * V)
- + ((nu ** 2) * (2 - 3 * (rho ** 2)) / 24.0)
- )
- * T
- )
- B = (
- 1
- + (1 / 24.0) * (((1 - beta) * logFK) ** 2)
- + (1 / 1920.0) * (((1 - beta) * logFK) ** 4)
- )
- VOL = (nu * logFK * A) / (x * B)
- return VOL
-
-
-if __name__ == "__main__":
- from analytics.option import BlackSwaption
- from analytics import CreditIndex
- from scipy.optimize import least_squares
-
- underlying = CreditIndex("IG", 28, "5yr")
- underlying.spread = 67.5
- exercise_date = datetime.date(2017, 9, 20)
- option = BlackSwaption(underlying, exercise_date, 70)
-
- strikes = np.array([50, 55, 57.5, 60, 62.5, 65, 67.5, 70, 75, 80, 85])
- pvs = np.array([44.1, 25.6, 18.9, 14, 10.5, 8.1, 6.4, 5, 3.3, 2.2, 1.5]) * 1e-4
-
- strikes = np.array([50, 55, 57.5, 60, 62.5, 65, 67.5, 70, 75, 80, 85, 90, 95, 100])
- pvs = (
- np.array(
- [
- 53.65,
- 37.75,
- 31.55,
- 26.45,
- 22.25,
- 18.85,
- 16.15,
- 13.95,
- 10.55,
- 8.05,
- 6.15,
- 4.65,
- 3.65,
- 2.75,
- ]
- )
- * 1e-4
- )
-
- def calib(x, option, strikes, pv, beta):
- alpha, rho, nu = x
- F = option.forward_spread
- T = option.T
- r = np.empty_like(strikes)
- for i, K in enumerate(strikes):
- option.strike = K
- option.sigma = sabr(alpha, beta, rho, nu, F, K, T)
- r[i] = option.pv - pv[i]
- return r
-
- prog = least_squares(
- calib,
- (0.3, 0.5, 0.3),
- bounds=(np.zeros(3), [np.inf, 1, np.inf]),
- args=(option, strikes, pvs, 1),
- )
|