Formulae for prices and Greeks for European (vanilla) puts in a Black-Scholes world

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See Black Scholes Greeks for notation.


Payoff, see MnBSPutPayoff



Price (value), see MnBSPutPrice



Delta (sensitivity to underlying), see MnBSPutDelta



Gamma (sensitivity of delta to underlying), see MnBSPutGamma



Speed (sensitivity of gamma to underlying), see MnBSPutSpeed



Theta (sensitivity to time), see MnBSPutTheta



Charm (sensitivity of delta to time), see MnBSPutCharm



Colour (sensitivity of gamma to time), see MnBSPutColour



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



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



Vega (sensitivity to volatility), see MnBSPutVega*



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



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



* 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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