A generic Black-Scholes-Merton python calculator (MIT licence). The main routine (black) is a generic solver that returns the value of the missing variable (usually implied volatility, but could be price, yield, etc)
black(cp=None, f=None, k=None, t=None, r=None, v=None, price=None, full=False, comp=inf):
""" General Purpose BSM machine. Leave one parameter blank and that is the parameter that will
be solved for.
cp = "c" for a call, anything else assumes a put
f = Forward Price of the underlying asset
k = Strike Price
t = Time until maturity (in years)
r = Interest rate
v = Implied volatility
comp = How many times interest is compounded a year (default = inf, i.e. continous rates)
full = If True, function returns a dictionary with price and all sensitivities
Otherwise only the calculated/calibrated parameter will be returned
"""
For examples, to solve for the implied volatility for a particular option:
black("c",k=100,f=101,t=1,r=0.05,price=5)
The library also has convenience functions such as impliedBlack that has volatility missing as an input, blackScholes that generates a forward by combining a dividend yield with the risk free rate and impliedBlackScholes which has the volatility input missing.
Finally we have impliedPair which relies only on the strike price, time to maturity, risk-free and the prices of a call options and a put options at the strike. This function solves for both the risk-free forward and the risk-neutral implied-volatility for this strike (European options only). See Wilmott for further info: Implied Volatility for same strike price for call and put