option pricing question

[dmo]

Quote from xflat2186:

Price swings in the underlying have an effect on the implied volatility which in turn effects the price of the options. That implied volatility effects the options prices on a curve. In a vacuum that curve would be bell shaped with the at the money being at the peak. Since implied volatility rises as the market falls and vice versa there is a skew such that the out of the money downside strikes trade at higher volatilities then the out of the money upside strikes. ALL CALLS AND PUTS IN THE SAME STRIKE SAME MONTH TRADE AT PARITY TO EACHOTHER AND ARE PRICED THE SAME IN RELATIVE TERMS.

That is all true and a good explanation. There are many explanations for the skew in the S&P500, but the one you cite is the best and makes the most sense IMHO.

I would add only that "in a vacuum," the probability distribution is lognormal, not normal, so that bell-shaped curve is off-center. In other words, if all strikes traded at the same implied volatility, the out-of-the-money put would be cheaper than the equally out-of-the-money call. If the S&P is at 1400, the 1350 put would be cheaper than the 1450 call if both traded at the same implied volatility.

 

[h hubbins]

thanks for the info guys! i was pretty puzzled.

 

[dmo]

Quote from Pita:

when the market is in an up swing/trend calls are higher priced than puts and vice versa.

In many contracts, the skew is somewhat changeable, as you say. As the underlying approaches a top, traders get excessively bullish, and they buy OTM calls and shun OTM puts. As a result, the upside skew steepens, and the downside skew weakens. The reverse happens as the underlying approaches a bottom.

However - strangely - that is NOT true of the options on S&P500. That skew is just rock-solid, it never changes. I don't know of another contract like it.

So I agree that the skew is the explanation to the original question asked in this thread. But watch the S&P500 option skew and you'll see that it's always the same.

 

[xflat2186]

The cost to carry a put vs a call is the true answer the skew, particularlly in the SPX just adds to it

 

[dmo]

Quote from xflat2186:

The cost to carry a put vs a call is the true answer the skew, particularlly in the SPX just adds to it

With one caveat - if we're talking about options on futures, there is no cost of carry of the underlying.

 

[commiebat]

Quote from xflat2186:

The cost to carry a put vs a call is the true answer the skew,

The cost to carry is much more visible on a 1400 strike than a 35 strike.

 

[xflat2186]

Quote from dmo:

With one caveat - if we're talking about options on futures, there is no cost of carry of the underlying.

SPX is not exactly an option on future.

 

[h hubbins]

well actually i was asking about the options on the futures. so does that mean this is all related to skew and not cost of carry?

sorry for not being more clear.

 

[dmo]

Quote from h hubbins:

well actually i was asking about the options on the futures. so does that mean this is all related to skew and not cost of carry?

sorry for not being more clear.

Yes. The cost of carry of the underlying should already be reflected in the price of the futures. Normally the futures trade at a premium to the cash for exactly that reason. So if you were talking about options on futures, then the entire explanation should be the skew.

 

[h hubbins]

thanks. about midway through my question i was going to ask if it was related to the dividends and interest but it seemed that should already be built into the futures premium.