[Quantlib-users] calculating second/third order greeks

[Edward L. <ed...@ed...>]

Hi,

I am trying to calculate some of the second and third order greeks using QuantLib. At this stage I am maintaining three BlackScholesMertonProcess processes (standard; one for increased volatility; one for increased underlying price) and using those for some of the functions.

That said, I am struggling with how I can apply this approach to greeks such as vomma, speed, color, ultima, etc. Does anyone have any suggestions? I also hope the other ones I've got are correct.

   # First order
    def delta(self):
        return self._ql_option.delta()

    def vega(self):
        return self._ql_option_for_vol_increase.NPV() - self._ql_option.NPV()

    def theta(self):
        return self._ql_option.theta()

    def lambda(self):
        return self._ql_option.delta() * (self._spot.value() / self._ql_option.NPV())

    def elasticity(self):
        return self.lambda()

    # rho: not implemented - not a priority
    # epsilon: not implemented - not a priority

    # Second order
    def gamma(self):
        return self._ql_option.gamma()

    def vanna(self):
        return self._ql_option_for_vol_increase.delta() - self._ql_option.delta()

    def charm(self):
        return self._ql_option_for_price_increase.theta() - self._ql_option.theta()

    # vomma: not implemented
    # veta: not implemented
    # vera: not implemented

    # Third order
    # speed: not implemented

    def zomma(self):
        return self._ql_option_for_vol_increase.gamma() - self._ql_option.gamma()

    # color: not implemented
    # ultima: not implemented

Thanks!