mattsta / pygreeks

calculate exact black-scholes option value using pytorch autograd and also calculate greeks using either autograd or numerical approximation

pygreeks: black-scholes greeks in python

pygreeks implements black-scholes and IV discovery in python using either exact derivatives from pytorch autograd or a fast numerical approximation.

pygreeks operates in one of two modes:

• you provide the strike, put/call, underlying, expiration then one of:
  • iv
  • npv

If you provide npv (usually the current option bid/ask midpoint is a safe bet if bids exist), then iv will be calculated for the strike at current expiration + iv + underlying.

If you provide iv, then npv will be calculated for the current expiration + iv + underlying.

Here's exact figures using derivatives to get the iv and all first order greeks for a current price:

>>> pygreeks.optionGreeksAuto(pygreeks.Option(kind='call', underlying=48, strike=49, expiry=(2/365), npv=0.55))
Option(kind='call', underlying=48, strike=49, expiry=0.005479452054794521, iv=0.6766163408740353, npv=0.5499992370605469, greeks=Greeks(theta=-0.22239099442958832, delta=0.34953978657722473, gamma=0.1539958268404007, vega=0.013154408894479275))

Here's approximate figures using two step numerical approximation:

>>> pygreeks.optionGreeksFast(pygreeks.Option(kind='call', underlying=48, strike=49, expiry=(2/365), npv=0.55))
Option(kind='call', underlying=48, strike=49, expiry=0.005479452054794521, iv=0.6766160239953531, npv=0.5499992370605469, greeks=Greeks(theta=-0.22254317168663496, delta=0.3495396503168968, gamma=0.15399597226320086, vega=0.01315440614997891))

The approximate (Fast) version runs about 40x faster than the pytorch version for IV calculations.

Usage

import pygreeks

Define an option using pygreeks.Option() with parameters described in the examples above, then run one or more of:

• pygreeks.optionGreeksAuto(option) for autograd greeks and IV
• pygreeks.optionGreeksFast(option) for numerical approximation greeks and IV (but may fall back to autograd IV if the approximation IV fails to converge)

License

pytorch implementation adapted from https://github.com/mgroncki/IPythonScripts/blob/master/PricingPyTorch/PlainVanillaAndBarriersCPU.ipynb (BSD)

numeric approximation is via py_vollib (MIT)

Any other features or improvements made available under Apache-2.0