This is a question from course cs 335.

Could you please help me solve this question?

1. (5 marks) (Arbitrage Pricing) Assume that a (no dividend} stock is currently traded at SD = $5 a share. At the end of three months T, it has a 99% chance of trading at ST : $7 and a 1% chance of trading at ST 2 $4 per share. Consider a derivative contract which pays the payoff min [max [ST K, D) ,0.5). Let the strike price K = $5 and assume that the risk free rate is zero. 1What is the fair value of this derivative contract? 'What is the delta hedging position for the writer of the option? Explain your