Synthetic Option

[ajsa]

Hi David,

Could you explain how to create a synthetic option using index futures?

Thanks.

 

[syaiful]

Hi Ajsa, :lol:

is it different than using Put-Call parity relationship ?

Thanks,

Syaiful

 

[ajsa]

Hi Syaiful,

I am not sure. but creating an option using Put-Call parity still needs another option, right? Do I miss anything? Please provide a quick reference if you think otherwise. There is an AIM requesting to create a synthetic option using index futures..

thanks.

 

[David Harper CFA FRM]

Syaiful, totally correct:

put-call parity: long call + lend PV strike = protective put
c+K*EXP[-rT] = p + S, such that
c = -K*EXP[-rT] + S + p
and synthetic call is given by = -K*EXP[-rT] + S + p = negative discounted strike (borrow cash) + S (buy stock) + p (by put)
i.e., borrow at the riskless rate the PV of the strike price (note how +discounted strike "lending" changes to -negative "borrowing) in order to fund the purchase of stock plus a put (expect the lending to fund most but not all of the purchase, the difference being equal to value of call)
....at expiration, repay the strike price. If S > Strike, future profit = S - K and put protects on the downside (equivelant to expired option)
....in short: synthetic call = borrow cash to fund a protective put

David

 

[syaiful]

Hi Ajsa, :lol:

for the example *type of question* please refer to GARP sample 2009 no 28

actually i am now working on *expected questions Syaiful's version*

and i *expected* this is one of question from Hull Chapter 9 that will be appear on November 2009


Regards,

Syaiful

 

[ajsa]

Hi David,

I was actually asking about buying insurance through a synthetic put through index futures (AIM 47.7). I read the reason synthetic option is better than regular option is it can customize the strike and maturity. If we borrow cash to fund a protective put, we still have the same issue of inflexibility. Plus it seems this does not involve index futures.

Thanks.

 

[David Harper CFA FRM]

Hi ajsa,

(I don't recognize the AIM; I just did a text search of "synthetic" and did not find this AIM. Can you source the assigned reading? ... )

...we can still apply the above in a variant with the forward: let S = F*EXP[-rT] and put call parity becomes:
c+discounted strike = p+discounted forward, such that
p = c + discounted strike - discounted forward

so synthetic put given by:
long call (strike @ delivery K) + lend strike + short (index) forward

in future, if index > delivery price, gain on call hedges loss on short forward.
If index < delivery, profit on short forward

...or i guess more direct is:
short the index futures and buy a call option (strike @ delivery price) to hedge the loss on the futures contract.

David

 

[ajsa]

Hi David,

Sorry for the confusion, here is the AIM:
"Describe how portfolio insurance can be created through option instruments and stock index futures."
It is in John Hull, Options, Futures, and Other Derivatives, Chapter 17, but I have found it is hard to follow when reading it..

Thanks.

 

[ajsa]

Hi David,

"short the index futures and buy a call option (strike @ delivery price) to hedge the loss on the futures contract. "
did you mean to hedge the loss on the portfolio? (synthetic put to protect portfolio)

So why does one want to create a synthetic put? it needs a call and a index future short, isn't it troublesome?

BTW this AIM is actually on Note4 p69:
"Describe how portfolio insurance can be created through option instruments and stock index futures
The typical approach to creating portfolio insurance is to acquire a put option. For example, a portfolio manager may buy a put on the S&P 500 index. The alternative is to create the option synthetically by shorting a futures contract."

Thanks,