Are Synthetic Options Truly Equivalent Options?
- Thread starter OddTrader
- Start date
I guess I have to post this again:
http://www.wilmott.com/messageview.cfm?catid=19&threadid=4301
PLEASE try reading the various proofs offered by Alan, as well as the one that appears in a nice Word document. Pretty PLEASE?
According to Weert:
Q
Since both the assumption c-p>S-Ke^-r(T-t) as well as c-p<S-Ke^-r(T-t) lead to arbitrage possibility, the put-call parity, c-p=S-Ke^-r(T-t), has to hold.
...
It is possible to synthetically create a forward by buying a call option and selling a put option with the forward price as the strike.
...
Since forwards do not cost anything it should also be the case that a call minus a put with the forward price as the strike is worth 0.
...
The put-call parity for non-divident paying stocks states:
c-p=S-Ke^-r(T-t).
The forward of a non-divident paying stock is
F=Se^r(T-t),
which shows that if the strike price for both the call and the put is the forward price (,?) the call minus the put, the synthetic, is worth 0.
In the same way, this can be proved for options on divident paying stocks. However, in this case the put-call parity is:
c-p=S-Ke^(r-d)(T-t)
where d is the divident yield.
In practice, one would only see synthetic forward on specific strikes, not necessarily on the forward price.
UQ
Q
Since both the assumption c-p>S-Ke^-r(T-t) as well as c-p<S-Ke^-r(T-t) lead to arbitrage possibility, the put-call parity, c-p=S-Ke^-r(T-t), has to hold.
...
It is possible to synthetically create a forward by buying a call option and selling a put option with the forward price as the strike.
...
Since forwards do not cost anything it should also be the case that a call minus a put with the forward price as the strike is worth 0.
...
The put-call parity for non-divident paying stocks states:
c-p=S-Ke^-r(T-t).
The forward of a non-divident paying stock is
F=Se^r(T-t),
which shows that if the strike price for both the call and the put is the forward price (,?) the call minus the put, the synthetic, is worth 0.
In the same way, this can be proved for options on divident paying stocks. However, in this case the put-call parity is:
c-p=S-Ke^(r-d)(T-t)
where d is the divident yield.
In practice, one would only see synthetic forward on specific strikes, not necessarily on the forward price.
UQ
No, nothing wrong, apologies...
The only violations of P-C parity I have experienced personally happened with some Eurodollar conversions (a bunch of flat positions, e.g. short call, long put, long contract). Some of the calls got exercised early (some dodgy margin optimization b-s), while I could actually find a bid for the put. I believe that's an example of what you're looking for, but I am not sure how helpful that might be.
OT, may I ask what you're trying to achieve by posting all these quotes?
Haven't we seen enough on the subject to put this one to bed?