diff options
Diffstat (limited to 'python/analytics/sabr.py')
| -rw-r--r-- | python/analytics/sabr.py | 133 |
1 files changed, 100 insertions, 33 deletions
diff --git a/python/analytics/sabr.py b/python/analytics/sabr.py index 4de15338..7d66f1da 100644 --- a/python/analytics/sabr.py +++ b/python/analytics/sabr.py @@ -3,59 +3,104 @@ import math import numpy as np
from numba import jit, float64
-@jit(float64(float64, float64, float64, float64, float64, float64),cache=True,nopython=True)
+
+@jit(
+ float64(float64, float64, float64, float64, float64, float64),
+ cache=True,
+ nopython=True,
+)
def sabr_lognormal(alpha, rho, nu, F, K, T):
- A = 1 + (0.25 * (alpha * nu * rho) + nu * nu * (2 - 3 * rho * rho) / 24.) * 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)
+ nulogFK = nu * math.log(F / K)
z = nulogFK / alpha
- x = math.log( ( math.sqrt(1-2*rho*z+z**2) + z - rho ) / (1-rho) )
+ x = math.log((math.sqrt(1 - 2 * rho * z + z ** 2) + z - rho) / (1 - rho))
VOL = (nulogFK * A) / x
return VOL
-@jit(float64(float64, float64, float64, float64, float64, float64),cache=True,nopython=True)
+
+@jit(
+ float64(float64, float64, float64, float64, float64, float64),
+ cache=True,
+ nopython=True,
+)
def sabr_normal(alpha, rho, nu, F, K, T):
if F == K:
V = F
- A = 1 + (alpha * alpha / (24. * V * V) + nu * nu * (2 - 3 * rho * rho) / 24.) * T
+ 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. * (V * V)) + ((nu * nu) * (2 - 3 * (rho * rho)) / 24.) ) * T
+ 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. * logFK2 + 1/24.
+ B = 1 / 1920.0 * logFK2 + 1 / 24.0
B = 1 + B * logFK2
VOL = (nu * logFK * A) / (x * B)
return VOL
-@jit(float64(float64, float64, float64, float64, float64, float64, float64),cache=True,nopython=True)
+
+@jit(
+ float64(float64, float64, float64, float64, float64, float64, float64),
+ cache=True,
+ nopython=True,
+)
def sabr(alpha, beta, rho, nu, F, K, T):
- if beta == 0.:
+ if beta == 0.0:
return sabr_normal(alpha, rho, nu, F, K, T)
- elif beta == 1.:
+ 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.*(V**2)) + (alpha*beta*nu*rho) / (4.*V) +
- ((nu**2)*(2-3*(rho**2))/24.) ) * T
- VOL = (alpha/V)*A
- elif F != K: # not-ATM formula
- V = (F*K)**((1-beta)/2.)
- 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.*(V**2)) + (alpha*beta*nu*rho)/(4.*V) +
- ((nu**2)*(2-3*(rho**2))/24.) ) * T
- B = 1 + (1/24.)*(((1-beta)*logFK)**2) + (1/1920.)*(((1-beta)*logFK)**4)
- VOL = (nu*logFK*A)/(x*B)
+ 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
@@ -70,8 +115,27 @@ if __name__ == "__main__": 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
+ 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
@@ -84,6 +148,9 @@ if __name__ == "__main__": 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))
+ prog = least_squares(
+ calib,
+ (0.3, 0.5, 0.3),
+ bounds=(np.zeros(3), [np.inf, 1, np.inf]),
+ args=(option, strikes, pvs, 1),
+ )
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