Post by Jefferson N. GlapskiPut call parity is model independent. The price of the calls and puts are
exogenous.
It actually isn't. you cannot compare across models. It is model free
in the sense that for those option types where Put/Call Parity holds
then any valid model for that option type should be constructed such
that Put/Call Parity holds (And even this is only true under the
usually Black Scholes model assumptions. If I no longer assume
completeness this doesn't hold for example and in reality completeness
doesn't exist, Actually Arb this is something to think about for
yourself as well. Often we can'tyhedge and option and thus cannot arb
it even if it is miss priced. This is not typically an issue for
exchange traded stock options but somehing to think about anyhow.)
To this point look at the relationship below. the last part of the
equation assumes riskless arbitrage which need not hold for all option
models. It is always assumed for most basic models but is not
necessary for more complex ones.
p = C - S + K e^(-r T).
Anyhow within the context of this discussion it should hold for most
commonly used stock option models.
That said if an option is American and I use black scholes to imply
the vol I am probably OK for the call as long as there is no dividends
but when I imply the vol for the put and compare, there is no reason
for them to match. This is not a violation of P/C parity it is simply
an artifact of having used an in appropriate model for the put.
Post by Jefferson N. GlapskiAnd yes, it is common for Black Scholes to be used by the market for vol
quotes. It is also a well-known fact that Black Scholes systematically
misprices certain types of options. If it misprices prices given volatility,
it misprices vol given price. It's not enough to make enough of a difference
to be meaningful in most cases.
I agree that in most cases the differenc is small. Just as the
difference is small between when I use bid vs ask inn most cases. The
problem is that it is not safe to assume it is always small and thus
when the resulting difference is not small it means there is an arb.
It just may not be the case.
Post by Jefferson N. GlapskiQuotes are usually bid. And bid/ask spreads in this case exceed that
difference.
Actually when you compute implied vol in and of itself for use say in
end of day mark to market for use say in FAS 133 valuations (I know
where you work so I assume you know what this is) you are usually
going to use mid market vols, same is true for risk management. Now
that said it is more desirable where I have both sides to use the one
most appropriate. If I am valuaing a short position, I should use
market ask vols to value it for FAS 133 for example as this is where I
could cover. Anyhow this is somewhat splitting hairs.
Post by Jefferson N. GlapskiPost by Investing4AllNow about the perpetual Put. First off it is not true that an
american call is worth more than a european call. It is true that an
american call cannot be worth less than a european call. This is not
the same thing. The same hold for a put. Now the argument that a
perpetual european put is worth zero is true. Unfortunately the same
is true for a perpetual europen call. This is obvious as you never
get to exercise so there can never be any cash flow associated with
either.
Just used it for a proof. Early exercise of a call on equities is not
optimal (except in Japan, arguably, depending on your realized rates).
Not true it is almost always optimal when dividends are being paid.
It doesn't require negative interest rates. In fact negative rates
violate the Black Scholes assumptions.
Post by Jefferson N. GlapskiPost by Investing4AllBut this is meaning less. Any finite put even very long dated (I just
ran it with expiry out 8000 years) will show the american put worth at
least as much as the eurpean and neither is worth zero.
I think you have this reversed. P>p.
Again, this is not correct. Consider. If I own an American option I
always have the option of holding it to maturity in which case the
payoff is identical to a european and the value gievn that expected
payoff is the same as a european. Now with an american put I have the
same option as the owner of a european put but I also own an extra
option to exercise early. The second option to exercise early must be
worth zero or greater it cannot be worth a negative value. Thus an
American Put is always worth at least as much as a European.
Anyhow I think this has been a worthwhile discussion and hopefully
some have learned something.
That said we need to keep it civil or I won't play. there is no point
going off about cost of education and stuff (I'll add a zero onto the
end to most people on here) and trying to rip each other to pieces.
That kind of mud slinging gets us nowhere except to a useless forum.
None of this on the board should be personal. There are no stupid
questions and if a statement is wrong we should simply make a case why
and debate it (As hard as it is to believe, even I can be wrong on
occasion.) We shouldn't be foaming at the mouth about it.
Paul Michaud
http://www.Investing4All.com
Providing Option Pricing Models, Forecasts and
GARCH Option Volatility Surfaces for over
10,000 stocks and indices from 43 exchanges around the world