Formulae for prices and Greeks for
European binary calls in a Black-Scholes world
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See Black Scholes Greeks
for notation.
Payoff, see MnBSBinaryCallPayoff
Price (value), see MnBSBinaryCallPrice
Delta (sensitivity to underlying), see MnBSBinaryCallDelta
Gamma (sensitivity of delta to underlying), see MnBSBinaryCallGamma
Speed (sensitivity of gamma to underlying), see MnBSBinaryCallSpeed
Theta (sensitivity to time), see MnBSBinaryCallTheta
Charm (sensitivity of delta to time), see
{Hpl|~/MnBSBinaryCallCharm.aspx|MnBSBinaryCallCharm}
Colour (sensitivity of gamma to time), see MnBSBinaryCallColour
Rho(interest) (sensitivity to interest rate), see MnBSBinaryCallRhoInterest
Rho(dividend) (sensitivity to dividend yield), see MnBSBinaryCallRhoDividend
Vega (sensitivity to volatility), see MnBSBinaryCallVega*
Vanna (sensitivity of delta to volatility), see MnBSBinaryCallVanna*
Volga (or Vomma) (sensitivity of vega to volatility), see MnBSBinaryCallVolga*
* Greeks like vega, vanna and Volga/vomma that involve
partial differentials with respect to are in some
sense ‘invalid’ in the context of Black-Scholes, since in its derivation we
assume that is constant. We
might interpret them as applying to a model in which was
slightly variable but otherwise was close to constant for all ,
etc.. Vega, for
example, would then measure the sensitivity to changes in the mean level of .
For some types of derivatives, e.g. binary puts and calls, it can be difficult
to interpret how these particular sensitivities should be understood.