A bank is offering an interest rate call with an expiration of 45 days. The call pays off based on 180-day LIBOR. The volatility of forward rates is 17 percent. The 45-day forward rate for 180-day LIBOR is 0.1322 and the exercise rate is 12 percent.
The risk-free rate for 45 days is 11.28 percent. All rates are continuously compounded. Use the Black model to determine how much the bank should receive for selling this call for every $1 million of notional principal.