Formulae for prices and Greeks for
European binary puts in a Black-Scholes world
[this page | pdf | references | back links]
See Black Scholes Greeks
for notation.
Payoff, see MnBSBinaryPutPayoff
![](I/BlackScholesGreeksBinaryPuts_files/image001.png)
Price (value), see MnBSBinaryPutPrice
![](I/BlackScholesGreeksBinaryPuts_files/image002.png)
Delta (sensitivity to underlying), see MnBSBinaryPutDelta
![](I/BlackScholesGreeksBinaryPuts_files/image003.png)
Gamma (sensitivity of delta to underlying), see MnBSBinaryPutGamma
![](I/BlackScholesGreeksBinaryPuts_files/image004.png)
Speed (sensitivity of gamma to underlying), see MnBSBinaryPutSpeed
![](I/BlackScholesGreeksBinaryPuts_files/image005.png)
Theta (sensitivity to time), see MnBSBinaryPutTheta
![](I/BlackScholesGreeksBinaryPuts_files/image006.png)
Charm (sensitivity of delta to time), see MnBSBinaryPutCharm
![](I/BlackScholesGreeksBinaryPuts_files/image007.png)
Colour (sensitivity of gamma to time), see MnBSBinaryPutColour
![](I/BlackScholesGreeksBinaryPuts_files/image008.png)
Rho(interest) (sensitivity to interest rate), see MnBSBinaryPutRhoInterest
![](I/BlackScholesGreeksBinaryPuts_files/image009.png)
Rho(dividend) (sensitivity to dividend yield), see MnBSBinaryPutRhoDividend
![](I/BlackScholesGreeksBinaryPuts_files/image010.png)
Vega (sensitivity to volatility), see MnBSBinaryPutVega*
![](I/BlackScholesGreeksBinaryPuts_files/image011.png)
Vanna (sensitivity of delta to volatility), see MnBSBinaryPutVanna*
![](I/BlackScholesGreeksBinaryPuts_files/image012.png)
Volga (or Vomma) (sensitivity of vega to volatility), see MnBSBinaryPutVolga*
![](I/BlackScholesGreeksBinaryPuts_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.