blackscholes

A Black-Scholes calculator for Python that includes up to the third-order Greeks.

Supports the Black-Scholes-Merton model, Black-76 model and option structures.

There is also a graphical interface available at: https://carlo.ai/tools/blackscholes

Installation

pip install blackscholes

Examples

Input variables

S = 55.0  # Asset price of 55
K = 50.0  # Strike price of 50
T = 1.0  # 1 Year to maturity
r = 0.0025  # 0.25% Risk-free rate
sigma = 0.15  # 15% Volatility
q = 0.0 # 0% Annual Dividend Yield

Call

from blackscholes import BlackScholesCall
call = BlackScholesCall(S=S, K=K, T=T, r=r, sigma=sigma, q=q)
call.price()  ## 6.339408
call.delta()  ## 0.766407
call.spot_delta() ## 0.7683
call.charm()  ## 0.083267

Put

from blackscholes import BlackScholesPut
put = BlackScholesPut(S=S, K=K, T=T, r=r, sigma=sigma, q=q)
put.price()  ## 1.214564
put.delta()  ## -0.23359
put.spot_delta() ## -0.23417
put.charm()  ## 0.083267

Black-76

The Black-76 model is often used specifically for options and futures and bonds. blackscholes also supports this model. To see all available greeks check out section 4. The Greeks (Black-76).

Call Example

from blackscholes import Black76Call
call = Black76Call(F=55, K=50, T=1, r=0.0025, sigma=0.15)
call.price()  ## 6.2345
call.delta()  ## 0.7594
call.vomma()  ## 45.1347

Put Example

from blackscholes import Black76Put
put = Black76Put(F=55, K=50, T=1, r=0.0025, sigma=0.15)
put.price()  ## 1.2470
put.delta()  ## -0.2381
put.vomma()  ## 45.1347

Structures

blackscholes offers the following six option structures:

• Straddle
• Strangle
• Butterfly
• Iron Condor
• Spreads
• Iron Butterfly

All structures have a long and short version. To learn more check out section 6. Option Structures.

Long Straddle Example

from blackscholes import BlackScholesStraddleLong

straddle = BlackScholesStraddleLong(S=55, K=50, T=1.0,
                                    r=0.0025, sigma=0.15)
straddle.price()  ## 7.5539
straddle.delta()  ## 0.5328

Binary options

Binary options are also called exotic, digital or bet options. blackscholes supports Greeks for binary calls and puts.

Contributing

We very much welcome new contributions! Check out the Github Issues to see what is currently being worked on.

Also check out Contributing in the documentation to learn more about contributing to blackscholes.