Equity cash dividend modelling#

[53]:

import torch
import numpy as np
import matplotlib.pyplot as plt

[54]:

from quant_analytics_torch.analytics import blackanalytics

[96]:

F = torch.tensor(100.)
K = torch.tensor(100.)
D = torch.tensor(5.)
sigma_adj = torch.tensor(0.3)
sigma_phy = torch.tensor(0.3)
tau = torch.tensor(1.0)

[97]:

black_v = blackanalytics.black(F-D,K-D,tau,sigma_adj)

[98]:

blackanalytics.impliedvolatility(black_v, F, K, tau)

[98]:

tensor(0.2849)

[99]:

x = torch.linspace(-0.5,0.5,21)
strikes = F*torch.exp(x)

[100]:

ivs = []
ivs_adj = []

for k in strikes:
    black_v = blackanalytics.black(F-D,k-D,tau,sigma_adj)
    ivs.append(blackanalytics.impliedvolatility(black_v, F, k, tau))

    black_p = blackanalytics.black(F,k,tau,sigma_phy)
    ivs_adj.append(blackanalytics.impliedvolatility(black_p, F-D, k-D, tau))

ivp = np.array(ivs)

[101]:

plt.plot(strikes, [sigma_adj]*len(strikes))
plt.plot(strikes, ivs)
plt.plot(strikes, ivs_adj)

[101]:

[<matplotlib.lines.Line2D at 0x2b4b22d8e10>]

../_images/examples_EquityCashDividends_8_1.png

[102]:

1/2 * sigma_adj * D / F

[102]:

tensor(0.0075)

[103]:

(np.array(ivs)[1:]-ivs[:-1])/(x[1:]-x[:-1])

[103]:

tensor([0.0105, 0.0102, 0.0098, 0.0095, 0.0091, 0.0088, 0.0085, 0.0082, 0.0079,
        0.0077, 0.0074, 0.0072, 0.0069, 0.0067, 0.0065, 0.0063, 0.0061, 0.0059,
        0.0057, 0.0055])