Model Parameters for European Call Option:

$S_0=55,x=60,r=3\mathrm{.}5\%($the continuously compounded interest rate per year$),T=0\mathrm{.}4$ years, and $=$

$30\%($annualized volatility$).$

Assignment Questions: In your Excel report, please answer the following four questions.

Q$1(25$ points$)$: $($Special case: A $20-$period flexible binomial model$)$:

Objective: Calculate the premium of a European call option over $20$ periods using the flexible binomial model.

Instructions: Based on our previous discussions, set the following parameters: $=ln\frac{\frac{x}{S_0}}{{}^2(T)},t=(\frac{T}{N}),$

$u=$exp$(\sqrt[\phantom{2}]{}t+{}^{2}t),d=$exp$(-\sqrt[\phantom{2}]{}t+{}^{2}t),(1+r_f)=$exp$(r\frac{T}{N}),$ and $p=\frac{1+r_f-d}{u-d}.$

With $N=20$ periods in the flexible binomial model, calculate and present the values of $,$

$q,$ and $B(ja$;$N,p).$ Then, compute the European call option premium, $C_{20},$ in the $20-$period flexible binomial model.

Excel Setup Instructions: In $Q1,$ we set $N=20$ periods.

Input the parameters $S_0,x,r,T,,$ in the top left corner $($or the first row of your Excel

spreadsheet$).$

In another row of your spreadsheet, set the following parameters in order of variables involved

$($from left to right columns$)$:

Ensure all results are clearly displayed in your spreadsheet based on the prior Instructions.