Source code for naginterfaces.library.examples.roots.contfn_brent_interval_ex

#!/usr/bin/env python3
"``naginterfaces.library.roots.contfn_brent_interval`` Python Example."

# NAG Copyright 2018-2019.

# pylint: disable=invalid-name

from naginterfaces.library import roots, specfun

def main():
    """
    Example for :func:`naginterfaces.library.roots.contfn_brent_interval`.

    Finds a zero of a continuous function using Brent's algorithm.

    >>> main()
    naginterfaces.library.roots.contfn_brent_interval Python Example Results.
    Implied volatility for an option with a given target price.
    The implied volatility for the target price of 12.35008695 is 0.09000000.
    """

    print('naginterfaces.library.roots.contfn_brent_interval '
          'Python Example Results.')
    print('Implied volatility for an option with a given target price.')

    # Initial guess for sigma:
    sigma = 0.15
    # Option-pricing parameters:
    S = 100.  # Spot price of the underlying asset;
    K = 90.   # Strike price;
    T = 1.5   # Time to expiry;
    r = 0.03  # Annual risk-free rate of interest;
    q = 0.015 # Annual continuous yield rate.
    # Target option price:
    target = 12.35008695
    # The (Black--Scholes--Merton European option) volatility function:
    bsm_f = lambda sigma: (
        specfun.opt_bsm_price('c', [K], S, [T], sigma, r, q)[0, 0] - target
    )

    print(
        "The implied volatility for the target price of "
        "{:1.8f} is {:1.8f}.".format(
            target, roots.contfn_brent_interval(sigma, bsm_f).x
        )
    )

if __name__ == '__main__':
    import doctest
    import sys
    sys.exit(
        doctest.testmod(
            None, verbose=True, report=False,
            optionflags=doctest.REPORT_NDIFF,
        ).failed
    )