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I have pretty much what you have Chili. So where's your confusion? Are you wondering why it doesn't look more like a smile? Personally, I prefer to call the chart of implied volatilities by strike the "implied volatility skew" rather than "smile," precisely because it doesn't always...

Are you talking about S&P 500 options? That doesn't sound right. The out of the money calls normally trade at a lower IV than the at-the-moneys, progressively lower at every higher strike. If you tell me what exactly you're looking at, and the month, I'll take a look and see if I see the...

The "smile" on indices is not much of a smile - more like a crooked smirk. Every strike price trades at a higher implied volatility than the strike above it, and a lower implied volatility than the strike below it. In other words, as you go from the OTM calls (highest strikes) to the OTM...

Amen to that. I advocate trading like a little old lady, but for size.

LOL, very well put. Best to sell flood insurance just after a flood. People will pay a big premium for it.

In stocks, 1 option is an option on 100 shares of stock. In futures, 1 option is an option on 1 futures contract. One-to-one relationship.

Lognormal distribution does not say that. Right idea, but not that extreme (the part in italics is completely wrong of course). Please see my previous post.

No, it isn't as likely to double as to be cut in half. It's a cumulative effect - which is why the lognormal distribution is also called a cumulative normal distribution. Think of it this way - let's say the futures are at 10, and you're comparing a 19 call with a 1 put. To get to 1, it is...

I'd just like to add that there's no law forcing anyone to use a lognormal distribution in option pricing. It's true that virtually every public-domain model is based on a lognormal distribution, but you could use a normal distribution if you wanted. And if you did, then an ATM straddle with...

Not sure I understand "higher strike nominal." Could you elaborate?

There are two factors that make the ATM straddle have a positive delta. First, as Walter says, is the effect of the lognormal distribution. That is true even if the cost of carry is zero, as is true of options on futures. The cost of carry effect - if there is a cost of carry - increases...

Right you are, it's the strike that matters, not whether it's a put or a call. A put and a call at the same strike is essentially the same thing. But it is true that every model I know of uses a lognormal distribution. And you've got to know the rules before you can learn how to break them...

Walter can speak for himself - but what he meant is that the theoretical value of the OTM put is less than that of the equally out-of-the-money call. Theory, of course, assumes that both options are trading at the same implied volatility - which in the real world they aren't, as your example shows.

Walter - from what you've written, you're obviously a man who knows his way around options - I can easily believe you were a floor trader. So I KNOW you know that the lognormal distribution causes the equidistant lower strike to be priced cheaper than the equidistant higher strike, assuming...

Walter - keep in mind that the original question asked why- if the futures were at 1400 - the 1375 call was more expensive than the 1425 put. The lognormal distribution you cited would actually have the opposite effect - it should make the 1375 calls cheaper than the 1425 puts. I think...

The total cost of carry of the underlying is actually the cost of carry minus the dividends. At the moment the S&P500 pays about 2% in dividends, while the T-bill rate is about the same. As a result, the true cost of carry is currently close to zero. And in fact, the futures are currently...

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.

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

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...

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...