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.