Modify Sample Application $\mathrm{G}$ in the DerivaGem Application Builder software to test the convergence of the price of the trinomial tree when it is used to price a 2-year call option on a 5 -year bond with a face value of 100 . Suppose that the strike price (quoted) is 100 , the coupon rate is $7 \%$ with coupons being paid twice a year. Assume that the zero curve is as in Table 32.2. Compare results for the following cases:
(a) Option is European; normal model with $\sigma=0.01$ and $a=0.05$
(b) Option is European; lognormal model with $\sigma=0.15$ and $a=0.05$
(c) Option is American; normal model with $\sigma=0.01$ and $a=0.05$
(d) Option is American; lognormal model with $\sigma=0.15$ and $a=0.05$.