API¶
-
src.calcbsimpvol.calcbsimpvol(arg_dict)[source]¶ calculates implied volatility surface or smile. Translated from MATLAB code. As it is a bare-metal package I would suggest to write an adapter class to feed the function.
- Parameters
arg_dict (dict) –
cp (ndarray) – int…..Call = [+1], Put = [-1]…[m x n] or [1 x 1]
P (ndarray) – float…Option Price Matrix…[m x n]
S (ndarray) – float…Underlying Price…[1 x 1]
K (ndarray) – float…Strike Price…[m x n]
tau (ndarray) – float…Time to Expiry in Years…[m x n]
r (ndarray) – float…Continuous Risk-Free Rate…[m x n] or [1 x 1]
q (ndarray) – float…Continuous Dividend Yield…[m x n] or [1 x 1]
- Returns
iv (ndarray) – float…The Implied Volatility…[m x n]
Examples
This is the first example which is also included separate file within the examples folder.
from calcbsimpvol import calcbsimpvol import numpy as np S = np.asarray(100) K_value = np.arange(40, 160, 25) K = np.ones((np.size(K_value), 1)) K[:, 0] = K_value tau_value = np.arange(0.25, 1.01, 0.25) tau = np.ones((np.size(tau_value), 1)) tau[:, 0] = tau_value r = np.asarray(0.01) q = np.asarray(0.03) cp = np.asarray(1) P = [[59.35, 34.41, 10.34, 0.50, 0.01], [58.71, 33.85, 10.99, 1.36, 0.14], [58.07, 33.35, 11.50, 2.12, 0.40], [57.44, 32.91, 11.90, 2.77, 0.70]] P = np.asarray(P) [K, tau] = np.meshgrid(K, tau) sigma = calcbsimpvol(dict(cp=cp, P=P, S=S, K=K, tau=tau, r=r, q=q)) print(sigma) # [[ nan, nan, 0.20709362, 0.21820954, 0.24188675], # [ nan, 0.22279836, 0.20240934, 0.21386148, 0.23738982], # [ nan, 0.22442837, 0.1987048 , 0.21063506, 0.23450013], # [ nan, 0.22188111, 0.19564657, 0.20798285, 0.23045406]]
#%% Plotting the results from mpl_toolkits.mplot3d import Axes3D import matplotlib.pyplot as plt m = np.log(S/K) fig = plt.figure() ax = fig.add_subplot(111, projection='3d') ax.scatter(m, tau, sigma) ax.set_xlabel('log Moneyness') ax.set_ylabel('Time Until Expiry') ax.set_zlabel('implied Volatility [% p.a.]') plt.show()
This is the second example which is also included separate file within the examples folder.
from calcbsimpvol import calcbsimpvol import numpy as np P = [[59.14, 34.21, 10.17, 16.12, 40.58], [58.43, 33.59, 10.79, 17.47, 41.15], [57.87, 33.16, 11.363, 18.63, 41.74], [57.44, 32.91, 11.90, 19.58, 42.27]] P = np.asarray(P) S = np.asarray(100) K = np.arange(40, 160, 25) tau = np.arange(0.25, 1.01, 0.25) K, tau = np.meshgrid(K, tau) cp = np.hstack((np.ones((4, 3)), -1 * np.ones((4, 2)))) # [Calls[4,3], Puts[4,2]] r = 0.01 * np.ones((4, 5)) * np.asarray([1.15, 1.10, 1.05, 1]).reshape((4, 1)) q = 0.03 * np.ones((4, 5)) * np.asarray([1.3, 1.2, 1.1, 1]).reshape((4, 1)) sigma = calcbsimpvol(dict(cp=cp, P=P, S=S, K=K, tau=tau, r=r, q=q)) print(sigma) # [[0.27911614, 0.23659105, 0.20714849, 0.21834553, 0.24225733], # [0.2797917 , 0.2315275 , 0.20249323, 0.21436123, 0.23823301], # [0.27436779, 0.22679618, 0.1987485 , 0.21097384, 0.23450519], # [0.26918174, 0.22235213, 0.19572994, 0.20807133, 0.2310324 ]]
#%% Plotting the results from mpl_toolkits.mplot3d import Axes3D # noqa: F401 unused import import matplotlib.pyplot as plt m = np.log(S/K) fig = plt.figure() ax = fig.add_subplot(111, projection='3d') ax.scatter(m, tau, sigma) ax.set_xlabel('log Moneyness') ax.set_ylabel('Time Until Expiry') ax.set_zlabel('implied Volatility [% p.a.]') plt.show()
References
Li, 2006, “You Don’t Have to Bother Newton for Implied Volatility”