blackscholes

Documentation structure:

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.

Currently only supports European options.

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% Volatiltiy
q = 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

Black76

The Black-76 model is often specifically used 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

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

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

Structures are combination of call and put options. Every option structure has a Long and Short version. To learn more check out section 6. Option Structures.

Long Straddle

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

Long Strangle

from blackscholes import BlackScholesStrangleLong

strangle = BlackScholesStrangleLong(S=55, K1=40, K2=50, T=1.0,
                                    r=0.0025, sigma=0.15)
strangle.price()  ## 6.3800
strangle.delta()  ## 0.7530

Long (Call) Butterfly

from blackscholes import BlackScholesButterflyLong

butterfly = BlackScholesButterflyLong(S=55, K1=40, K2=50, K3=60, 
                                      T=1.0, r=0.0025, sigma=0.15)
butterfly.price()  ## 3.9993
butterfly.delta()  ## -0.2336

Long Iron Condor

from blackscholes import BlackScholesIronCondorLong

iron_condor = BlackScholesIronCondorLong(S=55, K1=20, K2=25, K3=45, K4=50, 
                                         T=1.0, r=0.0025, sigma=0.15)
iron_condor.price()  ## 4.0742
iron_condor.delta()  ## 0.1572

Bull Spread

from blackscholes import BlackScholesBullSpread
bull_spread = BlackScholesBullSpread(S=55, K1=40, K2=50, T=1.0,
                                     r=0.0025, sigma=0.15)
bull_spread.price()  ## 8.8011
bull_spread.delta()  ## 0.2202

Bear Spread

from blackscholes import BlackScholesBearSpread
bear_spread = BlackScholesBearSpread(S=55, K1=50, K2=40, T=1.0,
                                     r=0.0025, sigma=0.15)
bear_spread.price()  ## 1.1740
bear_spread.delta()  ## -0.2202

Long Iron Butterfly

from blackscholes import BlackScholesIronButterflyLong
iron_butterfly = BlackScholesIronButterflyLong(S=55, K1=95, K2=100, K3=105, 
                                               T=1.0, r=0.0025, sigma=0.15)
iron_butterfly.price()  ## 4.9873
iron_butterfly.delta()  ## -0.0001

Short Iron Butterfly

from blackscholes import BlackScholesIronButterflyShort
iron_butterfly = BlackScholesIronButterflyShort(S=55, K1=95, K2=100, K3=105, 
                                                T=1.0, r=0.0025, sigma=0.15)
iron_butterfly.price()  ## -4.9873
iron_butterfly.delta()  ## 0.0001

Binary options

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