Python for Finance, 2nd Edition

Appendix B. BSM Option Class

Class Definition

The following presents a class definition for a European call option in the Black-Scholes-Merton (1973) model. The class-based implementation is an alternative to the one based on functions as presented in “Python Script”:

#
# Valuation of European call options in Black-Scholes-Merton model
# incl. vega function and implied volatility estimation
# -- class-based implementation
#
# Python for Finance, 2nd ed.
# (c) Dr. Yves J. Hilpisch
#
from math import log, sqrt, exp
from scipy import stats


class bsm_call_option(object):
    ''' Class for European call options in BSM model.

    Attributes
    ==========
    S0: float
        initial stock/index level
    K: float
        strike price
    T: float
        maturity (in year fractions)
    r: float
        constant risk-free short rate
    sigma: float
        volatility factor in diffusion term

    Methods
    =======
    value: float
        returns the present value of call option
    vega: float
        returns the vega of call option
    imp_vol: float
        returns the implied volatility given option quote
    '''

    def __init__(self, S0, K, T, r, sigma):
        self.S0 = float(S0)
        self.K = K
        self.T = T
        self.r = r
        self.sigma = sigma

    def value(self):
        ''' Returns option value.
        '''
        d1 = ((log(self.S0 / self.K) +
               (self.r + 0.5 * self.sigma ** 2) * self.T) /
              (self.sigma * sqrt(self.T)))
        d2 = ((log(self.S0 / self.K) +
               (self.r - 0.5 * self.sigma ** 2) * self.T) /
              (self.sigma * sqrt(self.T)))
        value = (self.S0 * stats.norm.cdf(d1, 0.0, 1.0) -
                 self.K * exp(-self.r * self.T) * stats.norm.