Appendix B. Call Option Class

Example B-1 contains a class definition for a European call option in the Black-Scholes-Merton (1973) model (cf. Chapter 3, and in particular Example 3-1).

Example B-1. Implementation of a Black-Scholes-Merton call option class
#
# Valuation of European call options in Black-Scholes-Merton Model
# incl. Vega function and implied volatility estimation
# -- class-based implementation
# bsm_option_class.py
#

from math import log, sqrt, exp
from scipy import stats

class 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
        return present value of call option
    vega : float
        return Vega of call option
    imp_vol: float
        return 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.cdf(d2, 0.0, 1.0))
        return value

    def vega(self):
        ''' Returns Vega of ...

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