In 60 days, a bank plans to lend $10 million for 180 days. The lending rate is LIBOR plus 200 basis points. The current LIBOR is 4.5 percent. The bank buys an interest-rate put that matures in 60 days with a notional principal of $10 million, days in underlying of 180 days, and a strike rate of 4.3 percent. The put premium is $4,000. What is the effective annual rate of the loan if at expiration LIBOR = 4.1 percent?
Answer and Explanation
The effective amount the bank parts with or lends at time of the loan is: $10,004,043 = $10,000,000 + $4,000 × (1 + (0.045 + 0.02) × (60/360))
If LIBOR at maturity equals 4.1 percent, the payoff of the put would be: payoff = ($10,000,000) × [max(0, 0.043 0.041) × (180/360) payoff = $10,000
The dollar interest earned is: $305,000=$10,000,000 × (0.041+0.02) × (180/360), and
EAR = [($10,000,000 + $10,000 +$305,000) / ($10,004,043)](365/180) - 1
EAR = 0.0640 or 6.40%
The effective amount the bank parts with or lends at time of the loan is: $10,004,043 = $10,000,000 + $4,000 × (1 + (0.045 + 0.02) × (60/360))
If LIBOR at maturity equals 4.1 percent, the payoff of the put would be: payoff = ($10,000,000) × [max(0, 0.043 0.041) × (180/360) payoff = $10,000
The dollar interest earned is: $305,000=$10,000,000 × (0.041+0.02) × (180/360), and
EAR = [($10,000,000 + $10,000 +$305,000) / ($10,004,043)](365/180) - 1
EAR = 0.0640 or 6.40%
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发表于 2008-9-16 17:04
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