1.The current price of a non-dividend paying stock is $50. Use a two-step tree to value an American put option on the stock with a strike price of $48 that expires in 12 months. Each step is 6 months, the risk free rate is 5% per annum (continuously compounding), and the volatility is 20%.What is the option price? Show work in detail and use a tree diagram (Use 4 decimal places).

2. Assume Koco Ltd current stock price is $70. The American one-year call option on the stock is trading at $20 with strike price of $70. If the one-year rate of interest is 10% p.a. (continuously compounding), is the call price free from arbitrage, assuming that the stock pays no dividends? What if the stock pays a dividend of $5 in one year?

3.Two firms X and Y are able to borrow funds as follows:

Firm A: Fixed-rate funding at 4% and floating rate at Libor-1%.

Firm B: Fixed-rate funding at 5% and floating rate at Libor+1%.

Assume A prefers fixed rate and B prefers floating rate. Show how these two firms can both obtain cheaper financing using a swap. What swap strategy would you suggest to the two firms if you were an unbiased advisor? What is the net cost to each party in the swap? Show your work in detail.