import math


def d_fhess_by_strike(underlying, strike, rate, maturity, vol):
    """d_fhess_by_strike
    second derivative of :math:`d_{i}\ (i = 1, 2)` with respect to :math:`K`,
    where :math:`K` is strike.

    .. math::
        \\frac{\partial^{2}}{\partial K^{2}} d_{1}(K)
        = \\frac{1}{S \sigma \sqrt{T} },

    where
    :math:`S` is underlying,
    :math:`\sigma` is vol,
    :math:`T` is maturity.

    :param float underlying:
    :param float strike:
    :param float rate:
    :param float maturity:
    :param float vol:
    :return: value of second derivative of :math:`d_{1}` or :math:`d_{2}`.
    :rtype: float
    """
    assert(maturity > 0.0)
    return 1.0 / (math.sqrt(maturity) * vol * strike * strike)