The function blackscholes computes the present value of an European call option without dividends under Black-Scholes model.

The function requires the value of the standard deviation. It can be calculated from the variance by taking the square root.

The hedge ratio is the ratio of the expected stock price at expiration to the current stock price.

There are strong assumptions on the Black-Scholes model. Use at your own risk. Refer to appropriate finance books for the list of assumptions.

Since blackscholes used to be part of the (now deprecated) finance package, for compatibility with older worksheets, this command can also be called using finance[blackscholes]. However, it is recommended that you use the superseding package name, Finance, instead: Finance[blackscholes].

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

$B≔\mathrm{blackscholes}\left(50.00\,49.00\,0.07\,\frac{199}{365}\,\mathrm{sqrt}\left(0.09\right)\right)\:$

$\mathrm{evalf}\left(B\right)$

$5.849179520$

$\mathrm{evalf}\left(\mathrm{blackscholes}\left(50.00+1.00\,49.00\,0.07\,\frac{199}{365}\,\mathrm{sqrt}\left(0.09\right)\right)\right)$

$6.511554996$

$\mathrm{evalf}\left(\mathrm{blackscholes}\left(50.00\,49.00+1.00\,0.07\,\frac{199}{365}\,\mathrm{sqrt}\left(0.09\right)\right)\right)$

$5.326914003$

$\mathrm{evalf}\left(\mathrm{blackscholes}\left(50.00\,49.00\,0.07+0.01\,\frac{199}{365}\,\mathrm{sqrt}\left(0.09\right)\right)\right)$

$5.994210290$

$\mathrm{evalf}\left(\mathrm{blackscholes}\left(50.00\,49.00\,0.07\,\frac{199+1}{365}\,\mathrm{sqrt}\left(0.09\right)\right)\right)$

$5.864587748$

$\mathrm{evalf}\left(\mathrm{blackscholes}\left(50.00\,49.00\,0.07\,\frac{199}{365}\,\mathrm{sqrt}\left(0.09+0.01\right)\right)\right)$

$6.072347530$

$f≔x\mapsto \mathrm{evalf}\left(\mathrm{blackscholes}\left(x\,49.00\,0.07\,\frac{199}{365}\,\mathrm{sqrt}\left(0.09\right)\right)\right)\:$

$U≔x\mapsto x\:$

$L≔x\mapsto \max \left(x-49.00\,0.\right)\:$

$\mathrm{plot}\left(\left\{'L\left(x\right)'\,'U\left(x\right)'\,'f\left(x\right)'\right\}\,x=0..100\,\mathrm{labels}=\left[\mathrm{`share\; price`}\,\mathrm{`value\; of\; call`}\right]\right)$

The Finance[blackscholes] command was introduced in Maple 15.

For more information on Maple 15 changes, see Updates in Maple 15.