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eee · 2018年06月11日

官网题目,关于二项式估值at the money interst rate call



Franco comments: “I think six-month call options on the six-month forward rate would probably be the cheapest solution. The price of the European-style option can be evaluated as the present value of the expected terminal option’s payoffs using the risk-adjusted periodic rate. Because Newport has indicated that its goal is to pay a maximum interest rate of 1.25% on the loan, we could also use interest rate put and call options. I believe the binomial model can be used to value interest rate options. Exhibit 1 shows the current interest rate information.”

EXHIBIT 1

Current six-month Libor1.00%
Six-month forward rate in six months1.15%




Q. Based on the information shown in Exhibit 1 and using a two-step binomial model to value the current at-the-money interest rate call option, the value of the underlying instrument at Node 0 would most likely be:

  1. 1.25%.
  2. 1.15%.
  3. 1.00%.

Solution

C is correct. When using the two-period binomial model to value interest rate options, the value of the underlying instrument at Node 0 is the spot rate. The spot rate (and the at-the-money strike price) is the current Libor rate of 1.00%.


答案说这句话说估值等于spot rate 是哪个知识点?我不记得了,请解释一下,谢谢!



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竹子 · 2018年06月12日

对于二叉树求interest rate option,我们的标的资产是spot rate,比如我们在6个月到期的时候,是将执行利率与市场中的6个月的spot rate相比来判断是否执行。所以underlying instrument is spot rate,在t=0时刻,spot rate=1

拓展一下,BSM模型是无穷多期二叉树,所以BSM的标的资产也是spot rate

但是BLACK MODEL中用的是forward price。所以如果这一题问的是black model,它的underlying是FRA,就选 1.15%

竹子 · 2018年06月12日

interest rate option的标的资产就是相同时间的LIBOR,这一题是6个月的option,那标的就是6个月的LIBOR,现在要求0时刻标的资产的value, 不就是现在市场上6个月LIBOR么?即1%

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