Formulae for prices and Greeks for European binary puts in a Black-Scholes world

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See Black Scholes Greeks for notation.


Payoff, see MnBSBinaryPutPayoff



Price (value), see MnBSBinaryPutPrice



Delta (sensitivity to underlying), see MnBSBinaryPutDelta



Gamma (sensitivity of delta to underlying), see MnBSBinaryPutGamma



Speed (sensitivity of gamma to underlying), see MnBSBinaryPutSpeed



Theta (sensitivity to time), see MnBSBinaryPutTheta



Charm (sensitivity of delta to time), see MnBSBinaryPutCharm



Colour (sensitivity of gamma to time), see MnBSBinaryPutColour



Rho(interest) (sensitivity to interest rate), see MnBSBinaryPutRhoInterest



Rho(dividend) (sensitivity to dividend yield), see MnBSBinaryPutRhoDividend



Vega (sensitivity to volatility), see MnBSBinaryPutVega*



Vanna (sensitivity of delta to volatility), see MnBSBinaryPutVanna*



Volga (or Vomma) (sensitivity of vega to volatility), see MnBSBinaryPutVolga*



* 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.


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