$5.$ Consider at$-$the$-$money American call and put on stock Y$.$ Both the call and the put are $6-$month to expiration. Current stock price is $$200$; and the stock does not pay any dividend in $6-$month. Interest rate is $10\%.$ The put option premium is $$8\mathrm{.}57.$

a$.$ What is the range of the call option premium, for which the trader has no arbitrage opportunities? $(5$ points$)$

b$.$ Suppose market price of the call is out of your range in a$.$ Please use a numeric example to briefly describe your arbitrage strategy and cash flows today and in $6$ months. $(6$ points$)$