bsm_smc.py

import numpy as np
import pandas as pd
import yfinance
import matplotlib.pyplot as mplt
from bs4 import BeautifulSoup
import dryscrape

iframe_url = 'http://www2.bmf.com.br/pages/portal/bmfbovespa/lumis/lum-taxas-referenciais-bmf-ptBR.asp'
session = dryscrape.Session()
session.visit(iframe_url)
response = session.body()
soup = BeautifulSoup(response, 'html.parser')

# Curva de Taxa de Juros
df_ettj = pd.read_html(
    str(soup.table),
    header=1,
   decimal=',',
   thousands='.',
    )[0]
df_ettj.columns = ['Dias', '252', '360']


# Volatilidade
data = yfinance.download(
    tickers = 'VALE3.SA',
    start="2018-08-08",
    end="2020-08-08",
    interval = '1d',
    treads = False
)

data['LogReturn'] = np.log(data['Close']
                            / data['Close'].shift(1))
data['Volatility'] =  data['LogReturn'].rolling(21).std() * np.sqrt(252)

# Exemplo: VALEI603	60,30 21/setembro
# Data do Cálculo: 08/agosto/2020

S0 = 60.45 # initial index level
K = 60.30 # strike price
T = 29/252 # time-to-maturity
r = df_ettj.loc[df_ettj['Dias'] == 29]['252'].values[0] / 100 # riskless short rate
sigma = data['Volatility'][-1]
I = 10000000 # number of simulations

# Valuation Algorithm
z = np.random.standard_normal(I)  # pseudorandom numbers
ST = S0 * np.exp((r - 0.5 * sigma ** 2) * T + sigma * np.sqrt(T) * z)
# index values at maturity
hT = np.maximum(ST - K, 0)  # inner values at maturity
C0 = np.exp(-r * T) * np.sum(hT) / I # Monte Carlo estimator

# Result Output
print("Valor teórico da Opção Européia %5.3f" % C0)