https://github.com/boyac/pyOptionPricing
Option pricing based on Black-Scholes processes, Monte-Carlo simulations with Geometric Brownian Motion, historical volatility, implied volatility, Greeks hedging
https://github.com/boyac/pyOptionPricing
blackscholes derivatives investment-banking option-pricing volatility
Last synced: about 7 hours ago
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Option pricing based on Black-Scholes processes, Monte-Carlo simulations with Geometric Brownian Motion, historical volatility, implied volatility, Greeks hedging
- Host: GitHub
- URL: https://github.com/boyac/pyOptionPricing
- Owner: boyac
- License: other
- Created: 2017-06-03T12:54:28.000Z (over 8 years ago)
- Default Branch: master
- Last Pushed: 2025-02-24T06:22:27.000Z (7 months ago)
- Last Synced: 2025-09-08T19:42:00.288Z (27 days ago)
- Topics: blackscholes, derivatives, investment-banking, option-pricing, volatility
- Language: Python
- Homepage:
- Size: 779 KB
- Stars: 312
- Watchers: 3
- Forks: 33
- Open Issues: 2
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# pyOptionPricing
A collection of Python scripts for option pricing and volatility calculations.
[](https://github.com/sponsors/boyac)
[](https://ko-fi.com/boyac)
**If you find this project helpful, please consider supporting its development!** Your contribution helps to maintain and expand this valuable resource for the options trading community.
## Description
This repository provides implementations of various option pricing models and volatility calculations in Python 2.7. It's a valuable resource for:
* Students learning about option pricing theory
* Quantitative analysts and traders
* Anyone interested in exploring financial modeling techniques
## Key Features
* **Traditional Historical Volatility Calculation:** Simple and easy-to-understand implementation.
* **Garman-Klass Historical Volatility:** More sophisticated volatility estimation.
* **Black-Scholes Model:** Classic option pricing model.
* **Exotic Option Example (Shout Options):** Demonstration of Monte Carlo approximation.
* **Clear and Commented Code:** Easy to follow and adapt for your own needs.
## Usage
To use these scripts, you'll need:
* Python 2.7
* pandas
* pandas_datareader
* scipy
Install the dependencies using pip:
```bash
pip install pandas pandas_datareader scipy
```
---
### Traditional Historical Volatility Calculation
```python
# -*- coding: utf-8 -*-
# @Author: boyac
# @Date: 2016-05-02 18:28:28
# @Last Modified by: boyac
# @Last Modified time: 2016-05-02 19:09:29
from pandas import np
import pandas_datareader.data as web
def historical_volatility(sym, days): # stock symbol, number of days
"Return the annualized stddev of daily log returns of picked stock"
try:
# past number of 'days' close price data, normally between (30, 60)
quotes = web.DataReader(sym, 'yahoo')['Close'][-days:]
except Exception, e:
print "Error getting data for symbol '{}'.\n".format(sym), e
return None, None
logreturns = np.log(quotes / quotes.shift(1))
# return square root * trading days * logreturns variance
# NYSE = 252 trading days; Shanghai Stock Exchange = 242; Tokyo Stock Exchange = 246 days?
return np.sqrt(252*logreturns.var())
if __name__ == "__main__":
print historical_volatility('FB', 30) # facebook: 0.296710526109
```
### Garman-Klass Historical Volatility
```python
# -*- coding: utf-8 -*-
# @Author: boyac
# @Date: 2016-05-02 18:28:28
# @Last Modified by: boyac
# @Last Modified time: 2016-05-02 19:09:29
from pandas import np
import pandas_datareader.data as web
def gk_vol(sym, days):
""""
Return the annualized stddev of daily log returns of picked stock
Historical Open-High-Low-Close Volatility: Garman Klass
sigma**2 = ((h-l)**2)/2 - (2ln(2) - 1)(c-o)**2
ref: http://www.wilmottwiki.com/wiki/index.php?title=Volatility
"""
try:
o = web.DataReader(sym, 'yahoo')['Open'][-days:]
h = web.DataReader(sym, 'yahoo')['High'][-days:]
l = web.DataReader(sym, 'yahoo')['Low'][-days:]
c = web.DataReader(sym, 'yahoo')['Close'][-days:]
except Exception, e:
print "Error getting data for symbol '{}'.\n".format(sym), e
return None, None
sigma = np.sqrt(252*sum((np.log(h/l))**2/2 - (2*np.log(2)-1)*(np.log(c/o)**2))/days)
return sigma
if __name__ == "__main__":
print gk_vol('FB', 30) # facebook: 0.223351260219
```
### Black-Scholes Model
```python
# -*- coding: utf-8 -*-
# @Author: boyac
# @Date: 2016-05-02 18:28:28
# @Last Modified by: boyac
# @Last Modified time: 2016-05-04 00:27:52
from __future__ import division
from scipy.stats import norm
from math import *
# Cumulative normal distribution
def CND(X):
return norm.cdf(X)
# Black Sholes Function
def BlackScholes(CallPutFlag,S,K,t,r,s):
"""
S = Current stock price
t = Time until option exercise (years to maturity)
K = Option striking price
r = Risk-free interest rate
N = Cumulative standard normal distribution
e = Exponential term
s = St. Deviation (volatility)
Ln = NaturalLog
"""
d1 = (log(S/K) + (r + (s ** 2)/2) * t)/(s * sqrt(t))
d2 = d1 - s * sqrt(t)
if CallPutFlag=='c':
return S * CND(d1) - K * exp(-r * t) * CND(d2) # call option
else:
return K * exp(-r * t) * CND(-d2) - S * CND(-d1) # put option
if __name__ == "__main__":
# Number taken from: http://wiki.mbalib.com/wiki/Black-Scholes期权定价模型
print BlackScholes('c', S=164.0, K=165.0, t=0.0959, r=0.0521, s=0.29) # 5.788529972549341
```
### Exotic Options Example: Shout Options by Monte Carlo Approximation
## Support
This project is made possible by the generous support of its users. If you find this project helpful, please consider:
[](https://github.com/sponsors/boyac)
[](https://ko-fi.com/boyac)
* Becoming a GitHub Sponsor
* Buying me a coffee on Ko-fi