fat_tails_and_their_impact_on_option_prices0

ef47f559-f5fc-42d6-a495-d75204f7beae.py

# usual suspects
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
import seaborn as sns
import scipy.stats as stats
import warnings

from scipy.integrate import simps
from scipy.interpolate import interp1d

# some config
%config Completer.use_jedi = False
warnings.filterwarnings('ignore')
sns.set()

# fetch index daily returns
DATA_PATH = './asset_data.csv'
df = pd.read_csv(DATA_PATH)
# set Date as dt format and index
df['Date'] = pd.to_datetime(df['Date'])
df.set_index('Date', inplace=True)
df = df[['SPX']]
# compute daily log returns
df['ret'] = np.log(df['SPX'] / df['SPX'].shift(1)).dropna()


# plot them
fig, ax = plt.subplots(ncols=1, figsize=(25,12))
sns.distplot(df['ret'], kde=False, fit=stats.norm, ax=ax, bins=400)
# label them
ax.set_title("SPX Daily Log Returns Distribution Plot", fontsize=24)
ax.set_xlabel("Daily Log Return", fontsize=20)
ax.set_xticklabels(['{:,.0%}'.format(x) for x in ax.get_xticks()], fontsize=18)
ax.set_ylabel("Density", fontsize=20);