A stock that pays no dividends is worth So = 50 euros today. 

The risk-free interest rate with continuous compounding is 3% for the maturity T = 2 months. Assume that, in two months, the stock can take one of the two values Sou = 53 euros or Sod = 48 euros. Calculate the price of a European put on the stock with maturity T and exercise price K= 51 euros.

2. The risk-free rates with annual compounding are currently 4% for all maturities. 

Calculate the price of a floorlet that pays in three years 1000 max(4%-R, 0) €, where R is the one year LIBOR rate with annual compounding that will be determined in two years from now. Assume the forward interest rate volatility for the corresponding period is 20% per year?

The risk-free rates with annual compounding are currently 5% for all maturities. 

Calculate the price of a swaption of maturity 6 years that gives the right to its holder to receive the fixed rate 4% in an annual swap of maturity 3 years and notional 100 €. Assume the forward swap rate volatility for the corresponding period is 20% per year?