Awesome question combining Options trading with discounting

[monsieuruzairo3]

Dear David Harper, CFA, FRM, CIPM

I am quite sure you would have seen this question earlier. Please let me know if my approach is correct,although I don't seem to get correct answer

A European-style call spread consists of a long position in the 105 strike call and a short position in the 115 strike call both maturing in 18 months. The options are on a stock index with an annualized dividend yield of 1% per annum. The interest rates are 4% (annual compounding) for 1 year and 5% (annual compounding) for 2 years. Under these circumstances, what is the number nearest the maximum value of this position today?
Choose one answer.
Choose one answer.
a. 9.5 Correct
b. 10 Incorrect
c. 9.29 Incorrect

d. 9.4 Incorrect

My appraoch
The Profit is 10(115-105). However this is realized at the end of 18 months. So we need to discount it back to today.

Convert 4%(T=1) to continuously compounded rate = 3.92%
Since 18 month spot rate is not given so I will use (5%) and multiply by 0.5 Continoulsy compounded rate of 5% = 4.88%

Therefore discounting factor = exp(.0392*1) * exp(.0488*0.5) = 1.06566
Discounted profit = 10/1.06566=9.38 ~ 9.4
However answer is 9.5

Where am i going wrong?

Best Uzi

 

[ShaktiRathore]

Value at end of t=18 months=max(St-105,0)-max(St-115,0)
@St>115=>value=St-105-(St-115)=10
105<St<115=>value=St-105 so max value=10
So max payoff that can occur in 18 months is 10.
Use discrete compounding it would had been given if continuous been used,its already mentioned annual compounding rather than being explicitly mentioned the continuous compounding.
Discounting factor would be (1+.04)^1*(1+.05/2)^.5=1.04*1.0124=1.0529
So discounted profit/payoff=10/1.0529=9.498~9.5
many thanks!!

 

[monsieuruzairo3]

Hi
Why is it (1+.05/2)^0.5. Shouldn't it be (1+0.05/2)^1 since half year rate is 2.5% and no. of periods is 1

 

[ShaktiRathore]

sorry for the mistake. i cant figure out the answer
thanks

 

[David Harper CFA FRM]

monsieuruzairo3 can you source these questions? I'm not sure it's an awesome question, at all, it looks imprecise; are those spot (zero) rates? and "what is the maximum value of this position today?" is awkward; e.g., is that present value of maximum payoff? value could imply something else. If the correct answer is 9.5, then the implied 18 month discount rate is apparently (10/9.5)^(1/1.5)-1 = 3.479% with annual compounding, which isn't (to me) obviously compatible with 4% and 5%. Not sure if they are using dividend yield. Also, the answers are too near together, so it's basically a discounting question. I don't think this question is awesome but I maybe am missing the art inside

 

[monsieuruzairo3]

Hi David,

This is an FRM 2002 question as per my knowledge. You can read it at http://www.docin.com/p-304997835.html (Question 1). Even I am quite unclear on the wordings.
Thanks for looking into it.Much appreciated

Best
Uzi

 

[David Harper CFA FRM]

Hi monsieuruzairo3 okay, thanks ... 2002, wow! okay, now I understand. We recommend ignoring any FRM test papers before 2009 (worst case 2008); working test papers prior to 2008, in my opinion, can be counterproductive. The FRM exam is relatively young, the early papers contain many imprecisions that can be misleading to the modern candidate. For example, early papers assume a 10-year coupon-bearing bond's duration is 7.0, but we know better than to make such an assumption (as before, I see two imprecisions in this question, and I don't see how trying to figure it out helps us). Thanks,

 

[acebhavik]

The questions seems quite vague, with lot of ambiguity. It really would help avoid solving such questions as David rightly says counterproductive. And when you multiply the rate by 0.5 for the 6 months it has to be the forward rate between year 1 and year 2.