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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.

 


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