A call options mature in six months is trading for $3. The stock underlying the call option is currently trading for $52 and will pay a dividend of...

A call options mature in six months is trading for $3.80. The stock underlying the call option is currently trading for $52 and will pay a dividend of $4 in five month. The risk-free rate of interest is 12% p.a. with continuous compounding. If the strike price of the option is $50 is there an arbitrage opportunity that can generate risk less profit. Explain from both European and American options perspective. If the dividend is paid in a month time does your answer change for American option?

(8 marks)