Calculate Implied Volatility of Stock Option Using Python

Implied volatility is a measure of the expected fluctuation in the price of a stock or option over a certain period of time. It is derived from the market price of the option and reflects the market's expectations for the stock's future price movements.

I will use Python and MongoDB for this tutorial since I have the stocks and options data stored in mongoDB.

In [2]:

import pymongo
from pymongo import MongoClient
import datetime
import pandas as pd

Let us initiate the mongo DB Connection.

In [22]:

client = MongoClient('mongodb://localhost:27017')
db = client['stocktwits']

At the writing of this tutorial, the date is Jan 6th, 2023. So let us get both the option and stock data from mongoDB.

Let us pick the option contract of strike 100 call expiring Jan 20, 2023

In [43]:

expirationDate  = datetime.datetime.strptime("2023-01-20","%Y-%m-%d")
option = list(db.tdameritrade.find({'contractName':'TSLA',\
                                    'strike':100.0,\
                                    'option_type':'call',\
                                   'expirationDate':expirationDate})\
              .sort([('added',pymongo.DESCENDING)]).limit(1))

In [44]:

option

Out[44]:

[{'_id': ObjectId('63b8383f458ed2075a6d9b74'),
  'symbol': 'TSLA_012023C100',
  'description': 'TSLA Jan 20 2023 100 Call',
  'exchangeName': 'OPR',
  'bid': 15.0,
  'ask': 15.2,
  'last': 15.19,
  'mark': 15.1,
  'bidSize': 221,
  'askSize': 69,
  'bidAskSize': '221X69',
  'lastSize': 0,
  'highPrice': 16.13,
  'lowPrice': 7.74,
  'openPrice': 0.0,
  'closePrice': 13.18,
  'totalVolume': 6855,
  'tradeDate': None,
  'tradeTimeInLong': 1673038767940,
  'quoteTimeInLong': 1673038799842,
  'netChange': 2.01,
  'volatility': 76.836,
  'delta': 0.811,
  'gamma': 0.016,
  'theta': -0.166,
  'vega': 0.061,
  'rho': 0.031,
  'timeValue': 2.13,
  'theoreticalOptionValue': 15.124,
  'theoreticalVolatility': 29.0,
  'optionDeliverablesList': None,
  'expirationDate': datetime.datetime(2023, 1, 20, 0, 0),
  'daysToExpiration': 14,
  'expirationType': 'R',
  'multiplier': 100.0,
  'settlementType': ' ',
  'deliverableNote': '',
  'isIndexOption': None,
  'percentChange': 15.27,
  'markChange': 1.92,
  'markPercentChange': 14.58,
  'intrinsicValue': 13.06,
  'pennyPilot': True,
  'inTheMoney': True,
  'mini': False,
  'nonStandard': False,
  'strike': 100.0,
  'open_interest': 12856,
  'option_type': 'call',
  'contractName': 'TSLA',
  'lastTradeDate': datetime.datetime(2023, 1, 6, 0, 0),
  'price_mult_oi': 205696,
  'price_mult_vol': 109680,
  'added': datetime.datetime(2023, 1, 6, 16, 0, 3, 8000),
  'change_in_open_interest': -12}]

In [45]:

#Let us calculate the market price of the option
price = (option[0]['bid'] + option[0]['ask'])/2.0
print(price)

15.1

Let us look at the Tesla stock price on Jan 6, 2023

In [64]:

list(db.eod_stock_data.find({'ticker':'TSLA'}).sort([('date',pymongo.DESCENDING)]).limit(1))

Out[64]:

[{'_id': ObjectId('63b89d2631dc9aead1ea7889'),
  'date': datetime.datetime(2023, 1, 6, 0, 0),
  'open': 103,
  'high': 114.39,
  'low': 101.81,
  'close': 113.06,
  'adjusted_close': 113.06,
  'volume': 219981652,
  'ticker': 'TSLA',
  'perchange': 2.47}]

There are several other ways to calculate the implied volatility of an option in Python, I will use py_vollib.

Using the implied_volatility() function from the py_vollib library: The py_vollib library is a Python library for option pricing that provides a number of functions for calculating option prices and implied volatilities. You can use the implied_volatility() function to calculate the implied volatility of an option as follows:

In [57]:

from py_vollib.black_scholes_merton.implied_volatility import implied_volatility

iv = implied_volatility(price, s, k, t, r, q, flag)

In this example, the input parameters are:

price: The option's market price.
s: The current price of the stock.
k: The option's strike price.
t: The time until expiration, expressed in years.
r: The risk-free interest rate, expressed as a decimal.
q: annualized continuous dividend rate.
flag: A string indicating whether the option is a call option ('c') or a put option ('p').

In [52]:

price = 15.1
s = 113.06
k = 100.0
t = 14/365.0
r = 0.035 #3.5% 10 year treasury rate<br>
q = 0
flag = 'c'

In [59]:

iv = implied_volatility(price, s, k, t, r, q, flag)
print(iv)

0.7799898996788112

There you go, the implied volatility of the option contract is ~78%

Calculate Implied Volatility of Stock Option Using Python

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