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Compound Options

Maximus_FRM2012

New Member
Hi David,

I'm going through your notes and I searched the forum but I can't find any where that details how compound options work. Can you please let me know if I have the logic correct:

For example, a call on a call option:
on the first maturity, the holder of the option has the following choices:
1. Choose to purchase another option for another strike or maturity
2. Excercise Option

On the second maturity:
1. Excercise the option if its in the money
2. Expires worthless

For put on a put:
The holder of the option on the first maturity can choose the following:
1. Can choose to sell another put option to the counter party for another strike and maturity
2. Excercise the option

on the second maturity:
1. the counter party can excercise the option
2. counter party has the option expire worthless

Please let me know if this is correct and if not, can you please give an example like above for a call on a call and put on a put to help solidify it.

Thank you.

Maximus
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi Maximus ... I do wish we had more detail on some of the exotics including compound options. From the 5a video:



With slight edits to your entry above:

For example, a call on a call (or call on a put) option:

On the first maturity (T1), the holder of the option can:
  1. Choose to purchase a call (or put) for strike price of K1, but will only do this if VALUE of the call (or put) at T1 is greater than strike; i.e., to exercise if and only if c(1)>K1 or p(1)>K1
  2. Otherwise, expires worthless
On the second maturity (T2):
  1. Exercise call if S2 > K2; or put if S2 < K2 (as usual!)
  2. Otherwise, expires worthless
For a put on a put (or put on call):

On the first maturity (T1), the holder of the option can:
  1. Choose to sell a put (or sell a call) for strike price of K1, but will only do this if VALUE of put (or call) at T1 is less than strike; i.e., to exercise if and only if c(1)<K1 or p(1)<K1
  2. Otherwise, expires worthless
on the second maturity (T2)
  1. the counter party will exercise the call if S2 > K2; or will exercise put if S2 < K2
  2. Otherwise, expires worthless
So, note that compound option requires a two events (a joint probability) in order to payoff:
  • call on an option requires S1 high/low enough to justify exercise at T1, PLUS S2 high/low enough to produce intrinsic value at T2
  • put on an option requires S1 to justify the writing (sale) of an option at T1, PLUS S2 high/low enough to expire OTM, so that "we" only collect the premium at T1 but our written option goes unexpired
I hope that helps (this will be useful to beef up this section in 2013). Thanks!
 
Last edited:

james 2

New Member
Hi Dave,
Just to clarify:

At T0, enter an option (p1) to purchase / sell an option (p2) at T1 for a small premium (p1)
At T1, decide whether to exercise option or expire worthless
If exercise, buy / purchase the option (p2) for a small premium & strike (determined at T0) that will expire at T2

Is that right? Is S1 in your example = premium of p2 + strike of p2? Thanks
 

David Harper CFA FRM

David Harper CFA FRM
Staff member
Subscriber
Hi James,

That's close, but please note (I think) the only difference: your p2 = my K1; i.e., the first strike price is a predetermined option premium. And, S1 represents the stock price at T1, so S1 has only an indirect role (at T1) by deciding whether the first option (at T1) should be exercised; at T2, S2 determines terminal ATM/OTM/ITM as usual. So, my agreement-tweak to your text reads:
  • At T0, pay premium (p1) in exchange for (to hold) an option to purchase/sell, at future T1, an option with a then-premium of p2=K1 (first strike is a future, optional premium)
  • At T1, decide whether to exercise option or expire worthless; for example, for a call-on-a-call, exercise if c(1)>K1, or in your notion, if c(1)>p1; i.e., if value of call option, at T1, is greater than predetermined price of option (aka, first strike price)
    • If exercise, buy / purchase the option for a premium, p2 = K1 (which was known at T0), an option (the "actual, vanilla" option) with strike of K2
 
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