利用した実際の市場データ

　⇒03/C21000@100 (2月9日先物価格20290)

出力結果：

C21000 = 99.65
delta = 0.21

コメント：

結果は（当然ながら）ほぼ一致。
ブラウザ開いて5分で試せるGoogle　Colab は素晴らしい。

ソースコード


import numpy as np
import chainer
from chainer import Variable
import chainer.functions as F

stock_price = 20290.0
strike = 21000.0
years = 1.0/12
risk_free_rate = 0.01
volatility = 0.143
n_paths = 100000
n_steps = 100

times = np.linspace(0, years, n_steps, dtype=np.float64)

r = risk_free_rate
v = volatility
k = strike
T = years
initial_stocks = Variable(stock_price * np.ones((n_paths,), dtype=np.float64))
currents = initial_stocks
for c, n in zip(times[:-1], times[1:]):
  dt = n - c
  zs = np.random.normal(0.0, 1.0, currents.shape)
  currents = currents * F.broadcast(np.exp((r - 0.5 * v * v) * dt + v * dt ** 0.5 * zs))

# call_price = F.average(exp(-r * T) * F.softplus(currents - k, beta=10)) # you should smooth the relu to calculate gamma
call_price = F.average(np.exp(-r * T) * F.relu(currents - k))  
deltas = F.sum(chainer.grad([call_price], [initial_stocks], enable_double_backprop=True)[0])

print(f'C21000 = {call_price.data:.2f}')
print(f'delta = {deltas.data:.2f}')