Consider the Black$-$Scholes model with the exercise, i$.$e$.$ maturity time, $T=1$ and the strike price $K=5.$

Construct an Excel spreadsheet for the values of the European call $C(0,S)$ and the European put $P(0,S)$ options for

$S=0\mathrm{.}1,0\mathrm{.}2,0\mathrm{.}3,$cdots,$9\mathrm{.}8,9\mathrm{.}9,10\mathrm{.}0$

when the bank interest rate $r$ is equal to

$r=0\mathrm{.}05.$

Verify numerically the Call$-$Put parity.

The spreadsheet should work for any other values of the parameters $S,r,T$ and $K.$

Repeat the above for the following values or the interest rate $r$ :

$r=0\mathrm{.}01,r=0\mathrm{.}02,r=0\mathrm{.}03,r=0\mathrm{.}04,r=0\mathrm{.}05,$

$r=0\mathrm{.}06,r=0\mathrm{.}07,r=0\mathrm{.}08,r=0\mathrm{.}09,r=0\mathrm{.}1.$

Analyse your results and write down your observations and conclusions.

Marks will be awarded for mathematical correctness and spredsheet desingn and usability.