Demystifying Stock Options Vega Using Python

The vega of an option is expressed as a percentage, and it represents the change in the option's price for a 1% change in the implied volatility of the underlying asset. For example, if an option has a vega of 0.20, this means that the price of the option is expected to increase by $0.20 for every 1% increase in the implied volatility of the underlying asset.

We will be using following modules to do this excercise.

pymongo (assuming mongodb is already installed)
opstrat Python library to calculate option geeks using Black Scholes

In [ ]:

!pip install opstrat

For this excercise let us look at Tesla options. We will caculate the Options geek for the following option contract...

Todays date is Jan 9, 2023
TSLA Jan 20 2023 100 Call

In [21]:

import pymongo
import datetime
from pymongo import MongoClient
client = MongoClient('mongodb://localhost:27017')
db = client['stocktwits']
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},\
                                   {'bid':1,'ask':1,'last':1,'daysToExpiration':1,\
                                    'description':1,'strike':1,'volatility':1})\
              .sort([('added',pymongo.DESCENDING)]).limit(1))

In [22]:

option

Out[22]:

[{'_id': ObjectId('63bc57d6458ed2500e7cef5d'),
  'description': 'TSLA Jan 20 2023 100 Call',
  'bid': 20.7,
  'ask': 20.9,
  'last': 20.5,
  'volatility': 82.941,
  'vega': 0.037,
  'daysToExpiration': 11,
  'strike': 100.0}]

In [17]:

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

Out[17]:

[{'_id': ObjectId('63bc91a3275fc68177ad4212'),
  'date': datetime.datetime(2023, 1, 9, 0, 0),
  'open': 118.96,
  'high': 123.52,
  'low': 117.11,
  'close': 119.77,
  'adjusted_close': 119.77,
  'volume': 188448460,
  'ticker': 'TSLA',
  'perchange': 5.93}]

In [33]:

import opstrat as op
import json

In [32]:

K = 100 #Excercise Price of the option
St = 119.77 #current stock price
r = 0.0425 #risk free interest rate 4.25%
t = 11 #time to expire in days
v = 82.9 #implied volatility
type = 'c' #put or call option
bsm=op.black_scholes(K=K, St=St, r=r, t=t, 
                     v=v, type='c')
print(json.dumps(bsm,indent=2))

{
  "value": {
    "option value": 98.8702676900665,
    "intrinsic value": 98.87,
    "time value": 0.00026769006649374205
  },
  "greeks": {
    "delta": 1.0,
    "gamma": 1.0670964994225347e-34,
    "theta": -2.4335304744443113e-05,
    "vega": 3.8243193031313692e-34,
    "rho": 0.006298549463267629
  }
}

As we can see above, the above code outputs not only vega but all the option Geeks.

Demystifying Stock Options Vega Using Python

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