Question $3.$ A stock has current price $S_0=50.$ A butterfly spread on the stock is the payoff

$f_T=\{\begin{array}{ccc}0,& if& S_T{K}_1,\\ S_T-K_1,& if& K_1=K_3,\end{array}$

at maturity time $T,$ where $S_T{K}_1=30,K_3=602log(1\mathrm{.}25)5\%u=\frac{1}{d}t=0,1,2t=1t=2u=1\mathrm{.}25,d=0\mathrm{.}8$widehat$(p)=0\mathrm{.}4724$