[옵션] 만기별 옵션의 내재확률 시각화하기 (Feat. Asymmetry님)
Asymmetry님의 [Repository] #002 옵션내재확률 구하기글을 참조하여, 만기별 옵션 내재확률분포를 시각화하고, 인터랙티브 차트로 구성하는 코드를 작성해봄
만기를 세개까지 동시에 비교할 수 있도록 하고, 현물 가격을 세로선으로 표시하도록 수정
굳이 인터랙티브 차트를 추가 구성해 본 이유는
마우스를 갖다대면 내재확률(PDF)와 누적확률(CDF)가 나오기 때문에 만기에 특정 행사가 내에서 마감할 확률의 구간 추정에 용이하기 때문일 것 같아서임.
spx_quotedata 받아서 어떻게든 혼자 해보려고 Cursor 고문하다가 포기하려던 무렵, Asymmetry님이 옛날에 올려주셨던 코드를 발견해서 마개조함. (감사합니다 비대칭좌...)
이제 이를 어떻게 해석해서 실전적인 마켓뷰로 반영할 수 있는지 연구해보자.
코드전문
import pandas as pd
import numpy as np
from scipy.interpolate import interp1d, UnivariateSpline
from scipy.ndimage import gaussian_filter1d
from scipy.stats import norm, skew, kurtosis
import matplotlib.pyplot as plt
from matplotlib.ticker import FuncFormatter
from scipy.optimize import brentq
from scipy.integrate import cumulative_trapezoid
import datetime
from datetime import datetime
import plotly.graph_objects as go
from plotly.subplots import make_subplots
def is_third_friday(date):
return date.weekday() == 4 and 15 <= date.day <= 21
# Time difference calculation: seconds -> minutes -> years
def calculate_time_to_expiry(expiration_datetime):
current_datetime = datetime.now()
time_difference = (expiration_datetime - current_datetime).total_seconds() / 60 # Convert seconds to minutes
time_in_years = time_difference / 525600 # Convert minutes to years
return time_in_years
# Modified function to handle expiration filtering and time delta calculation
def process_expiration_data(option_data, target_dates):
results = {}
spotPrice = get_spot_price(file_path)
for target_date in target_dates:
print(f"\nProcessing data for expiration date: {target_date}")
# Filter for expiration date and identify if it's the third Friday
data_date = option_data[option_data['Expiration Date'] == target_date].copy()
if is_third_friday(target_date):
# Print a message confirming that we are excluding SPXW
print(f"Third Friday identified for {target_date}, only taking SPX (excluding SPXW).")
data_date = data_date[~data_date['Calls'].str.contains('SPXW')] # Exclude SPXW if third Friday
else:
print(f"Not the third Friday. Both SPX and SPXW are included for {target_date}.")
# Apply expiration datetime and calculate time to expiry in years
data_date['Expiration DateTime'] = data_date.apply(assign_expiration_datetime, axis=1)
expiration_datetime = data_date['Expiration DateTime'].iloc[0]
T = calculate_time_to_expiry(expiration_datetime) # Time to expiration in years
print(f"Time to Expiration: {T} years")
# Clean and filter valid data
data_date = data_date.dropna(subset=['Bid', 'Ask', 'Bid.1', 'Ask.1'])
data_date = data_date[(data_date['Bid'] > 0) & (data_date['Ask'] > 0) &
(data_date['Bid.1'] > 0) & (data_date['Ask.1'] > 0)]
# Continue with further steps such as calculating mid prices, implied volatility, etc.
# ...
# Store results for plotting and comparison later
results[target_date] = {
'spot_price': spotPrice,
'time_to_expiry': T,
# Other results you compute...
}
return results
def assign_expiration_datetime(row):
exp_date = row['Expiration Date']
if 'SPXW' in row['Calls']: # PM-settled SPXW (weekly options expire at 4:00 PM)
return datetime(exp_date.year, exp_date.month, exp_date.day, 16, 0)
else: # AM-settled SPX (standard options expire at 9:30 AM)
return datetime(exp_date.year, exp_date.month, exp_date.day, 9, 30)
def implied_volatility(option_price, S, K, T, r, option_type='call'):
def bs_price(sigma):
if sigma <= 0:
return np.nan
d1 = (np.log(S / K) + (r + 0.5 * sigma**2) * T) / (sigma * np.sqrt(T))
d2 = d1 - sigma * np.sqrt(T)
if option_type == 'call':
price = S * norm.cdf(d1) - K * np.exp(-r * T) * norm.cdf(d2)
else:
price = K * np.exp(-r * T) * norm.cdf(-d2) - S * norm.cdf(-d1)
return price
def objective_function(sigma):
return bs_price(sigma) - option_price
try:
implied_vol = brentq(objective_function, 1e-6, 5, maxiter=1000)
except (ValueError, RuntimeError):
implied_vol = np.nan
return implied_vol
def bs_price(S, K, T, r, sigma, option_type='call'):
sigma = max(sigma, 1e-6)
d1 = (np.log(S / K) + (r + 0.5 * sigma**2) * T) / (sigma * np.sqrt(T))
d2 = d1 - sigma * np.sqrt(T)
if option_type == 'call':
price = S * norm.cdf(d1) - K * np.exp(-r * T) * norm.cdf(d2)
else:
price = K * np.exp(-r * T) * norm.cdf(-d2) - S * norm.cdf(-d1)
return price
def calculate_implied_pdf(prices, strikes):
interp_func = interp1d(strikes, prices, kind='cubic', fill_value='extrapolate')
fine_strikes = np.linspace(min(strikes), max(strikes), 500)
prices_fine = interp_func(fine_strikes)
price_d2 = np.gradient(np.gradient(prices_fine, fine_strikes), fine_strikes)
return price_d2, fine_strikes
def normalize_pdf(pdf, strikes):
pdf = np.maximum(pdf, 0)
total_prob_before = np.trapezoid(pdf, strikes)
if total_prob_before == 0:
total_prob_before = 1e-6
pdf_normalized = pdf / total_prob_before
cdf = cumulative_trapezoid(pdf_normalized, strikes, initial=0)
cdf_normalized = cdf / cdf[-1]
return pdf_normalized, cdf_normalized
def normalize_pdf_within_zoomed_range(pdf, strikes, total_prob_zoomed):
pdf_normalized = pdf / total_prob_zoomed
cdf_zoomed = cumulative_trapezoid(pdf_normalized, strikes, initial=0)
cdf_zoomed_normalized = cdf_zoomed / cdf_zoomed[-1]
return pdf_normalized, cdf_zoomed_normalized
def get_spot_price(filename):
with open(filename, 'r', encoding='utf-8') as optionsFile:
optionsFileData = optionsFile.readlines()
spotLine = optionsFileData[1]
spotPrice_str = spotLine.split('Last:')[1].split('Change:')[0].strip()
spotPrice = float(spotPrice_str.replace(',', ''))
return spotPrice
def find_percentile(strikes, cdf, percentile):
idx = np.abs(cdf - percentile / 100).argmin()
return strikes[idx]
# Load the data
file_path = r'spx_quotedata.csv'
option_data = pd.read_csv(file_path, skiprows=3)
# Parse and filter by expiration date
option_data['Expiration Date'] = pd.to_datetime(option_data['Expiration Date']).dt.date
# Define the three target dates
target_dates = [pd.Timestamp('2025-06-27').date(), pd.Timestamp('2025-07-18').date(), pd.Timestamp('2025-08-15').date()]
results = process_expiration_data(option_data, target_dates)
# Get spot ...
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