The Vera of an option or a portfolio of options measures Rho's sensitivity to volatility.

The BlackScholesVera command computes the Vera of a European-style option with the specified payoff function.

The parameter $S_0$ is the initial (current) value of the underlying asset. The parameter T is the time to maturity in years.

The parameter K specifies the strike price if this is a vanilla put or call option. Any payoff function can be specified using the second calling sequence. In this case the parameter P must be given in the form of an operator, which accepts one parameter (spot price at maturity) and returns the corresponding payoff.

The sigma, r, and d parameters are the volatility, the risk-free rate, and the dividend yield of the underlying asset. These parameters can be given in either the algebraic form or the operator form. The parameter d is optional. By default, the dividend yield is taken to be 0.

$\mathrm{with}\left(\mathrm{Finance}\right)\:$

$\mathrm{BlackScholesVera}\left(100\,100\,1\,\mathrm{\sigma }\,r\,0\,'\mathrm{call}'\right)$

$-\frac{25\sqrt{2}{\ⅇ}^{-\frac{{\left({\mathrm{\sigma }}^2+2r\right)}^2}{8{\mathrm{\sigma }}^2}}\left({\mathrm{\sigma }}^2+2r\right)}{{\mathrm{\sigma }}^2\sqrt{\mathrm{\pi }}}$

$\mathrm{BlackScholesVera}\left(100\,100\,1\,0.3\,0.05\,0\,'\mathrm{call}'\right)$

$\mathrm{-40.05125392}$

$\mathrm{BlackScholesVera}\left(100\,t\mapsto \max \left(t-100\,0\right)\,1\,\mathrm{\sigma }\,r\,0\right)$

$-\frac{25\sqrt{2}{\ⅇ}^{-\frac{{\left({\mathrm{\sigma }}^2+2r\right)}^2}{8{\mathrm{\sigma }}^2}}\left({\mathrm{\sigma }}^2+2r\right)}{{\mathrm{\sigma }}^2\sqrt{\mathrm{\pi }}}$

$\mathrm{BlackScholesVera}\left(100\,t\mapsto \max \left(t-100\,0\right)\,1\,0.3\,0.05\,0\right)$

$\mathrm{-40.05125413}$

$\mathrm{Vera}≔\mathrm{BlackScholesVera}\left(100\,100\,1\,\mathrm{\sigma }\,r\,0\,'\mathrm{call}'\right)$

$\mathrm{Vera}≔-\frac{25\sqrt{2}{\ⅇ}^{-\frac{{\left({\mathrm{\sigma }}^2+2r\right)}^2}{8{\mathrm{\sigma }}^2}}\left({\mathrm{\sigma }}^2+2r\right)}{{\mathrm{\sigma }}^2\sqrt{\mathrm{\pi }}}$

$\mathrm{plot3d}\left(\mathrm{Vera}\,\mathrm{\sigma }=0..1\,r=0..1\right)$

$\mathrm{BlackScholesVera}\left(100\,120\,1\,0.3\,0.05\,0\,'\mathrm{put}'\right)$

$37.10151683$

$\mathrm{BlackScholesVera}\left(100\,t\mapsto \max \left(120-t\,0\right)\,1\,0.3\,0.05\,0\,0\right)$

$37.10151683$

$\mathrm{Vera}≔\mathrm{BlackScholesVera}\left(S\left[0\right]\,100\,T\,0.1\,0.05\,0\,'\mathrm{call}'\right)\:$

$\mathrm{plot3d}\left(\mathrm{Vera}\,T=1.0..0\,S\left[0\right]=0..200\,'\mathrm{labels}'=\left[''Time\; To\; Maturity''\,''Spot\; Price''\,''Value''\right]\,'\mathrm{colorscheme}'=\left[''zgradient''\,\left[''Black''\,''White''\,''Red''\right]\right]\,'\mathrm{thickness}'=0\right)$

Hull, J., Options, Futures, and Other Derivatives, 5th. edition. Upper Saddle River, New Jersey: Prentice Hall, 2003.

The Finance[BlackScholesVera] command was introduced in Maple 2015.

For more information on Maple 2015 changes, see Updates in Maple 2015.