Tango Bank has contracted to lend $80 million to Delta Co. in three months’ time. This loan will be for a period of six

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Tango Bank has contracted to lend $80 million to Delta Co. in
three months’ time. This loan will be for a period of six months.
To hedge against the risk of interest rates dropping, Tango has
purchased an interest rate put option. The put option has an
exercise rate of 2.15% and a maturity of three months. The
underlying forward rate is based on the LIBOR, which has a current
term structure of
# days
LIBOR
90
2%
270
2.3%
The terms of the LIBOR specify 30 days in a month and 360 days
in a year. The volatility on the underlying forward rate is 0.25.
Tango uses the Black Model to estimate the call premium.
a.
Calculate the contract premium the bank must pay for this put
option.
b.
Suppose that in three months’ time, the six-month LIBOR turns out
to be 2%. What is the annualized rate of return on Tango’s position
with the put option?