SABR Model Pricing Engine in Python QuantLib

Question

I am looking for a SABR model pricing engine in Python QuantLib setting. I do know that it exists in C++ version, but not sure if available in Python. Any suggestion/feedback with respect to Python source code will be greatly appreciated!. Thanks!

Answer 1

Here is a simple example that might be useful. Basically finding parameters for a given section. Some of the parameters might be assumed at start instead of calibrated.

import QuantLib as ql
import matplotlib.pyplot as plt
import numpy as np
from scipy.optimize import minimize

strikes = [105, 106, 107, 108, 109, 110, 111, 112]
fwd = 120.44
expiryTime = 17/365
marketVols = [0.4164, 0.408, 0.3996, 0.3913, 0.3832, 0.3754, 0.3678, 0.3604]

params = [0.1] * 4
def f(params):
    vols = np.array([
        ql.sabrVolatility(strike, fwd, expiryTime, *params)
        for strike in strikes
    ])
    return ((vols - np.array(marketVols))**2 ).mean() **.5

cons=(
    {'type': 'ineq', 'fun': lambda x:  0.99 - x[1]},
    {'type': 'ineq', 'fun': lambda x: x[1]},    
    {'type': 'ineq', 'fun': lambda x: x[3]}
)

result = minimize(f, params, constraints=cons)
new_params = result['x']

newVols = [ql.sabrVolatility(strike, fwd, expiryTime, *new_params) for strike in strikes]
plt.plot(strikes, marketVols, marker='o', label="market")
plt.plot(strikes, newVols, marker='o', label="SABR")
plt.legend();