A stock which doesnt pay dividends has a spot price of 53. You have entered a 2-year long forward contract at this spot price, while the interest rate is 5% per annum with continuous compounding.

1. What is the initial value of the forward contract?

2. What is the forward price?

3. Six months later, the price of the stock is 57 and the risk-free interest rate is still 5%. What are the forward price and value of the forward contract?

4. In the market, the price of the forward is currently 2.43, how can you strategize to earn a profit?

Suppose you are pricing a European put option using the binomial model. The stock price is $102, the strike price is $100, the maturity T is two years, the stock's volatility is 15%, and the risk-free rate is 3%. The stock's dividend yield is 2% and it pays only one dividend between now and maturity.

5. Calculate the value of the put option described above.