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.