Formulae for prices and Greeks for
European binary calls in a Black-Scholes world
[this page | pdf | references | back links]
See Black Scholes Greeks
for notation.
Payoff, see MnBSBinaryCallPayoff
![](I/BlackScholesGreeksBinaryCalls_files/image001.png)
Price (value), see MnBSBinaryCallPrice
![](I/BlackScholesGreeksBinaryCalls_files/image002.png)
Delta (sensitivity to underlying), see MnBSBinaryCallDelta
![](I/BlackScholesGreeksBinaryCalls_files/image003.png)
Gamma (sensitivity of delta to underlying), see MnBSBinaryCallGamma
![](I/BlackScholesGreeksBinaryCalls_files/image004.png)
Speed (sensitivity of gamma to underlying), see MnBSBinaryCallSpeed
![](I/BlackScholesGreeksBinaryCalls_files/image005.png)
Theta (sensitivity to time), see MnBSBinaryCallTheta
![](I/BlackScholesGreeksBinaryCalls_files/image006.png)
Charm (sensitivity of delta to time), see
{Hpl|~/MnBSBinaryCallCharm.aspx|MnBSBinaryCallCharm}
![](I/BlackScholesGreeksBinaryCalls_files/image007.png)
Colour (sensitivity of gamma to time), see MnBSBinaryCallColour
![](I/BlackScholesGreeksBinaryCalls_files/image008.png)
Rho(interest) (sensitivity to interest rate), see MnBSBinaryCallRhoInterest
![](I/BlackScholesGreeksBinaryCalls_files/image009.png)
Rho(dividend) (sensitivity to dividend yield), see MnBSBinaryCallRhoDividend
![](I/BlackScholesGreeksBinaryCalls_files/image010.png)
Vega (sensitivity to volatility), see MnBSBinaryCallVega*
![](I/BlackScholesGreeksBinaryCalls_files/image011.png)
Vanna (sensitivity of delta to volatility), see MnBSBinaryCallVanna*
![](I/BlackScholesGreeksBinaryCalls_files/image012.png)
Volga (or Vomma) (sensitivity of vega to volatility), see MnBSBinaryCallVolga*
![](I/BlackScholesGreeksBinaryCalls_files/image013.png)
* 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.