Actuarial Outpost > MFE American Option forumla using Compound Option
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#1
07-30-2012, 11:28 PM
 Nanook Member SOA Join Date: May 2012 Posts: 115
American Option forumla using Compound Option

Please excuse my formatting for this question:

CoP = Call on Put
PoC = Put on Call

I know the formula for an American Call option is:
C(Amer) = S - Ke^-rt + CoP

What is the formula for an America Put option using compound option?
P(Amer) = Ke^-rt - S + PoC ????
#2
07-31-2012, 12:07 AM
 Epsilon5 CAS SOA Join Date: Jun 2012 Posts: 19

The ASM manual states that most American options don't have a closed-form formula, and that the call with a single discrete dividend (the formula you cited) is an exception.

Since the American put may be worth more than a European put after the single discrete dividend (where the American call was equal to its European counterpart), I don't think that the value you proposed for the American put will work.

Please correct me if I'm wrong.
#3
07-31-2012, 02:29 AM
 Math Member Join Date: Jan 2011 Posts: 292

American options can be priced that way because it might be worth exercising right before a divident is paid. A put does not follow that same reasoning, hence we really don't have a formula in terms of compound options. I am not aware of one.
#4
07-31-2012, 04:30 AM
 MusaAli Member CAS SOA Join Date: Nov 2011 Posts: 114

Did u actually come across a question on that? cuz i haven't seen any yet :/
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#5
07-31-2012, 08:44 AM
 Nanook Member SOA Join Date: May 2012 Posts: 115

I did not come across a question like that (and now I know why). I was just worrying too much trying to prepare myself in case I did.

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