Actuarial Outpost Comparing Options Time to Expiry question
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 Investment / Financial Markets Old Exam MFE Forum

#1
11-01-2017, 11:10 PM
 Peter T.W. Chen CAS SOA Non-Actuary Join Date: Oct 2017 Posts: 15
Comparing Options Time to Expiry question

I have a question on ASM 10th edition Chapter 7 P.93 Example 7C.

For a nondivedend paying stock with price 21:
(i) The continuously compounded risk-free raye is 4%.
(ii) A European 3-month put option on the stock with strike price 20 costs 1.00.
(iii) A European 6-month put option on the stock with strike price 20.30 costs 0.90.
You take advantage of arbitrage. Assume that you sell one 3-month put option and follow the optimal strategy, and that the stock price is 19 after 3 months and 21 after 6 months.
Determine your net profit after 6 months.

I cannot understand the answer on the manual, can anyone help?
Let's fight for 2018 Mar MFE exam!! Gook Luck All!

Last edited by Peter T.W. Chen; 11-02-2017 at 01:35 AM..
#2
11-01-2017, 11:40 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,971

What is given as the answer?
#3
11-01-2017, 11:50 PM
 Peter T.W. Chen CAS SOA Non-Actuary Join Date: Oct 2017 Posts: 15

Quote:
0.1*exp(0.04*0.5) - 20*exp(0.04*0.25) + 21 = 0.9010
I know the first and the third term, but how to explain the second one?
#4
11-02-2017, 01:11 AM
 Academic Actuary Member Join Date: Sep 2009 Posts: 8,971

Quote:
 Originally Posted by Peter T.W. Chen 0.1*exp(0.04*0.5) - 20*exp(0.04*0.25) + 21 = 0.9010 I know the first and the third term, but how to explain the second one?
You sold a put with strike 20. It is exercised at time 3 months. Assume you borrow the money to cover.
#5
01-11-2018, 09:03 PM
 BartimaeusOfUruk SOA Join Date: Nov 2017 Location: Iowa Studying for FAP Posts: 20 Blog Entries: 3

Time 0:
3 month put with strike 20 is sold
6 month put with strike 20.3 is bought
Net cash flow time 0 = +0.1

Time 3/12:
Borrower exercises put
Net cash flow: -20

Time 6/12:
Bought put option expires worthless.
We sell stock that was "put" back on us at time 3/12Time 0:
3 month put with strike 20 is sold
6 month put with strike 20.3 is bought
Net cash flow time 0 = +0.1

Net cash flow: +21

AV of all cash flows: 0.1*exp(0.04*0.5) - 20*exp(0.04*0.25) + 21 = 0.9010

From a logical point of view- I find this easy to follow.
However, I would have naturally done:

Time 0:
3 month put with strike 20 is sold
6 month put with strike 20.3 is bought
Net cash flow time 0 = +0.1

Time 3/12:
Borrower exercises put
Net cash flow: -1

Time 6/12:
Bought put option expires worthless.
Net cash flow: 0

AV of all cash flows: 0.1*exp(0.04*0.5) - 1*exp(0.04*0.25) = -.8879

I don't feel like I've discovered any other problems where the put is valued in the manor this solution does...

 Tags comparing option, mfe, time to expiry