I look at put options for SPY. I see some options with high implied volatility and some with much lower implied volatility.

Intuitively, options with higher implied volatility should be priced higher (relative to their strike price) than those with lower implied volatility.

I feel that implied volatility is a property of the stock and shouldn't be dependent of the strike price. Is the Black-Scholes model inadequate? Is there an easy arbitrage opportunity (short high implied volatility, buy low implied volatility)? Am I missing something fundamental?

Yes. As you get further OTM, you will see higher implied volatility.

Higher implied volatility means that they are priced relatively higher in respect to their distance from the strike. It is just math.

That would be great! Then we could all get rich!!!

The "volatility smile" (worth googling) and "volatility smirk" (also worth googling) exist because there isn't payout symmetry.

Yes, but the "moneyness of options" (worth googling) is included in it. Further from strike price means higher implied volatility is correct according to the model.

Volatility smirk isn't included in it, which is a weakness of the model. It also assumes a lognormal distribution, which is a further weakness (tails are thicker than a lognormal distribution).

Nope.

Probably just the volatility smile and volatility smirk thingamajigs.

Thanks, will look into those. Is there some objective measure of expected profit/loss for options (assuming they're priced correctly)?

I'm wondering about the potential of buying put options for hedging a portfolio, but I don't really know how much it would cost (beyond fees).

They are generally priced at a bid/ask spread that makes them unprofitable.

You can easily calculate the payouts given a price of the underlying at expiration, but no one I know has access to the price of the price at expiration ahead of time.

Hedging costs money on average. The price of buying put options is precisely the price of the ask of the put (plus fees, minus the possibility that you will be filled between the bid and ask) - that is something you can easily calculate.

I mean, if the stock/market drops significantly, the put option could be considered to have cost a negative amount of money (i.e. turn a profit).

Yes, of course. That is easily calculable.

I get that it is easily calculated after the fact (in hindsight), but is there any reasonable measure of expected cost for a put option?

You can use half of the distance between the bid and ask

This is called kurtosis.

The cost of buying a put is known. The future price of a put is unknown.

Yes.

If you assume the perfect correctness of the Black Scholes model and the Efficient Market Hypothesis, should the EV of a put option be 0?

Financial markets are not 100% completely efficient. The theory is important academically and some markets are more efficient than others but nevertheless the efficient market theory is not 100% reality.

Hence the "If you assume" part.

Yes in that case the ev is zero. You are also assuming zero transaction costs fwiw

More generally, you just need to assume EMH (which also implies no arbitrage). BS is just a popular option model.

No. According to EMH, taking on risk is supposed to be +ev and selling a put is offloading risk onto another agent, so it should be -ev.

FYP. More blatantly wrong information from BtM, shocking. See tables I and II in http://www.people.hbs.edu/jcoval/pap...ionreturns.pdf

You didn't actually read the paper, right? You do know that the "-" in front of the returns in Table II isn't a dash, but is actually a minus sign, right?!?

I was going to put the relevant parts of the quote in bold for clarity, but that would require that I just bold the entire thing.

You can also look up the PUT (Put Write Index), which shows positive returns from selling puts. Interestingly, selling (aka writing) puts is the opposite of buying puts. This link shows a very pretty graph of the opposite of buying SPX puts: https://www.cboe.com/micro/put/putwrite.pdf

Edit: I am somewhat surprised that this isn't all common knowledge.

Edit 2: You are just ****ing with me, right? Like, "let's see if I can make the monkey actually type out the alphabet and seek out supporting documentation when he claims 'the alphabet starts with abc'."

EMH is not the same as efficient frontier. Even in the context of the efficient frontier, ev is the not the same as the mean-variance tradeoff. EV is a "trading" term, mean-variance is a investment term. Buying/selling an option at its true "intrinsic value" (mid price?), in theory has 0 ev, regardless what effect it may have on an overall portfolio.

What do you want us to see?

You're defending this?

lol. I typed "selling"?!?

Didn't realize that the other dude did a fyp where he fixed it to "buying". Yes, buying a put is offloading risk. Selling a put is taking on risk. Durr.

EMH doesn't disallow profit, which is what I think he was trying to ask. You won't find that you can purchase options for their intrinsic value in real life. In options the intrinsic value is the amount the option is in the money.

That I'm a bonehead and typed selling instead of buying.

Doesn't it? I'd think it does when it comes to options - as it's a zero sum game.

Also I don't think this is what was meant by intrinsic value.

Zero sum doesn't mean that the components are all zero expected profit.

For instance, you can do a synthetic long by buying at-the-money calls and selling an equal number of at-the-money puts. That theoretically has exactly the same profit profile as a long position, which is positive.

Not entirely sure what he specifically meant, but options have intrinsic and extrinsic value.