Formulae for prices and Greeks for
European (vanilla) calls in a Black-Scholes world
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See Black Scholes Greeks
for notation.
Payoff, see MnBSCallPayoff
Price (value), see MnBSCallPrice
Delta (sensitivity to underlying), see MnBSCallDelta
Gamma (sensitivity of delta to underlying), see MnBSCallGamma
Speed (sensitivity of gamma to underlying), see MnBSCallSpeed
Theta (sensitivity to time), see MnBSCallTheta
Charm (sensitivity of delta to time), see MnBSCallCharm
Colour (sensitivity of gamma to time), see MnBSCallColour
Rho(interest) (sensitivity to interest rate), see MnBSCallRhoInterest
Rho(dividend) (sensitivity to dividend yield), see MnBSCallRhoDividend
Vega (sensitivity to volatility), see MnBSCallVega}*
Vanna (sensitivity of delta to volatility), see MnBSCallVanna*
Volga (or Vomma) (sensitivity of vega to volatility), see MnBSCallVolga*
* 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.