A stock price is currently $80. It is known that at the end of four months it will be either $75 or $88. The risk free rate is 6 percentage per annum with continuous compounding. What is the value of a four-months European put option that is currently $1 out-of-the-money? Use no-arbitrage arguments and show the labeled tree. In a two period model (each period is one year) the current stock price is $25/share. The gross rate of return on the stock over each period is either +40% or -20% while the single period rate of interest is 10%. a) Price a European put option on the stock with a strike of $30/share that expires at the end of the second period? b) Price an American put with the same characteristic as the one above? Does it every make sense to exercise the put at the end of the first period? A European at-the-money call option on a currency has four years until maturity. The exchange rate volatility is 10%, the domestic risk-free rate is 2% and the foreign risk-free rate is 5%. The current exchange rate is 1.2000. a) What is the value of that call option (Use the Black Scholes Model)? b) Assume that in the question 3 above the option is a put, other things things remaining same, what would be the value of that put option (use the Black Scholes Model)