3. The current term structure of quarterly forward rates is given by f;(0)=0.01+0.0003x(j-1), j = 1, ,120. Use the Black's formula to price a cap and a swaption with the same notional value of $1m. Note that the payment frequency is a quarter year for caps and half a year for swaps. 3.1. Calculate the 10-year swap rate (The fixed leg has semi-annual payment). 3.2. Price the 10-year maturity cap with the strike rate to be the 10-year swap rate (such a cap is called at-the-money-forward cap). Take the cap volatility to be 25%. 3.3. Calculate the market prevailing swap rate for in-5-to-10 forward swap. 3.4. Price the in-5-to-10 ATM swaption on the payer's swap (i.e., maturity of the option: 5 years; tenor of the underlying swap: 10 years, strike rate: market prevailing swap rate for the in-5-to-10 forward swap). Assume a 25% swap-rate volatility. 3. The current term structure of quarterly forward rates is given by f;(0)=0.01+0.0003x(j-1), j = 1, ,120. Use the Black's formula to price a cap and a swaption with the same notional value of $1m. Note that the payment frequency is a quarter year for caps and half a year for swaps. 3.1. Calculate the 10-year swap rate (The fixed leg has semi-annual payment). 3.2. Price the 10-year maturity cap with the strike rate to be the 10-year swap rate (such a cap is called at-the-money-forward cap). Take the cap volatility to be 25%. 3.3. Calculate the market prevailing swap rate for in-5-to-10 forward swap. 3.4. Price the in-5-to-10 ATM swaption on the payer's swap (i.e., maturity of the option: 5 years; tenor of the underlying swap: 10 years, strike rate: market prevailing swap rate for the in-5-to-10 forward swap). Assume a 25% swap-rate volatility