Actuarial Outpost Rational early exercise question (MFE)
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 Investment / Financial Markets Old Exam MFE Forum

#1
12-15-2016, 01:12 PM
 karenyoung SOA Join Date: Aug 2016 Location: Irvine, California Studying for FAP Final Assessment College: UCLA Posts: 14
Rational early exercise question (MFE)

Hi! I'm stuck on a problem near the beginning of the MFE ASM manual so I'm hoping it's easy enough to get a quick response

A 182-day American call option on a stock has strike price 100. The continuously compounded risk-free interest rate is 4%. A dividend is payable on day 91. Determine the lowest dividend for which early exercise may be rational.

I thought it was K(1-e^(-0.04*0.5)) - PV(dividends) < 0, so that:
(dividend)*e^(-0.04*0.25) > 100(1-e^-0.02)
dividend = 2

This isn't correct! Can anybody help?
#2
12-15-2016, 01:53 PM
 ALivelySedative Member CAS Join Date: Dec 2013 Location: Land of the Pine College: UNC-Chapel Hill Alum Favorite beer: Red Oak Posts: 3,160

You should be using T=.25 instead of .5 I believe. Exercise would be immediately before the dividend payment on day 91 (or .25 years).

(Conveniently working on the same section this morning).
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#3
12-15-2016, 07:22 PM
 karenyoung SOA Join Date: Aug 2016 Location: Irvine, California Studying for FAP Final Assessment College: UCLA Posts: 14

Yeah the answer key used t=0.25 but I was just confused as to why the point of view of the problem was right before the dividend (around 90 days) rather than the beginning of the option (around 180 days).

Thank you though!
#4
12-16-2016, 04:38 AM
 Shagust2108 Member SOA Join Date: Jul 2016 Studying for FAP College: University of Hong Kong Posts: 44

Quote:
 Originally Posted by karenyoung Yeah the answer key used t=0.25 but I was just confused as to why the point of view of the problem was right before the dividend (around 90 days) rather than the beginning of the option (around 180 days). Thank you though!
The negative impact of early exercising is losing the protection of future stock price fluctuation plus the interest earned on the strike price. That is why we want to postpone the date of early exercise (if you would ever want to early exercise) possible. So we choose to exercise right before the dividend is paid rather than the beginning of option.
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