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eee · 2019年05月24日

官网题目关于effective rate



On 16 March 2012, First Citizen Bank (FCB) approached Silva for advice on a loan commitment. At that time, FCB had committed to lend $100 million in 30 days (on 15 April 2012), with interest and principal due on 12 October 2012, or 180 days from the date of the loan. The interest rate on the loan was 180-day Libor + 50 bps, and FCB was concerned about interest rates declining between March and April. Silva advised FCB to purchase a $100 million interest rate put on 180-day Libor with an exercise rate of 5.75% and expiring on 15 April 2012. The put premium was $25,000. Libor rates on 16 March 2012 and 15 April 2012 were 6% and 4%, respectively. The option was exercised on 15 April 2012, and the payoff was received on 12 October 2012. FCB has asked for a written evaluation of the success of the strategy.


C is correct. The effective annual rate is calculated as follows:

Future value of put premium on 15 April:

$25,000[1+(0.06+0.005)(30/360)]=$25,135.42$25,000[1+(0.06+0.005)(30/360)]=$25,135.42

Effective loan outlay = $100,000,000 + $25,135.42 = $100,025,135.42

Loan interest:

$100,000,000[(0.04+0.005)(180/360)]=$2,250,000$100,000,000[(0.04+0.005)(180/360)]=$2,250,000

Put Payoff:

$100,000,000[max(0,0.05750.04)(180/360)]=$875,000$100,000,000[max(0,0.0575−0.04)(180/360)]=$875,000

Effective interest = $2,250,000 + $875,000 = $3,125,000

Effective annualized loan rate:

(100,000,000+3,125,000100,025,135)365/1801=0.0638


关于期权费的复利不太理解,既然支付期权费时点libor是6%,为什么期权费要用libor+50bps考虑时间价值呢?



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企鹅_品职助教 · 2019年05月25日

这个地方何老师说过,如果严谨一些题目中会直接说用libor+之前给的spread. 但是即使题目中不说,也是要加上spread来算的。

具体来说,

对于call ,投资者买了call,是为了将来可以以确定的利率来借钱的,所以投资者支付了premium,支付的这笔钱相当于是提前用了未来的本金,那么就需要支付贷款利息,所以需要用贷款利率复利。(我们在计算的时候,也是将premium复利之后抵减本金的)

对于put,因为银行为了买put会支付premium,如果不支付这笔premium,银行可以将这笔钱贷出去,赚利息,赚的利息=LIBOR+spread。现在支付了premium, 相当于失去了赚利息的机会成本,所以我们要按这个机会成本进行复利,才能得到effective costs

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