I'd argue they're not (based on modeling the probability of the underlying price). There is nothing necessarily untrue about the statement (assuming ample liquidity), both the option holder and the option writer will make money if the contract goes to 1-delta. Actually, you can take that a step further and say the market maker's counter-parties on the outright both prior to and on expiration can all make money on their respective trades. Which means that (and not to condescend to @JackRab, but for the benefit of others) options price need not reflect the actual statistical probability of the price in the underlying; the sole dictate is they not present an arbitrage opportunity (frequently violated, but quickly rectified). And if you subscribe to any sort of technical or fundamental analysis theory, options pricing that reflects the price probability distribution of the underlying will present an arbitrage opportunity.
Edge in understanding Distributions?
- Thread starter jordanwrong
- Start date
@beerntrading it doesn't matter whether there is or isn't an arbitrage opportunity.... volatility is the main contributor to the calculation of option prices. Which basically dictates the probability distribution, with roughly 66% falling within +1/-1 sigma... 90% within +2/-2 sigma... 99% 3 sigma. This is what gives the options price/vega/gamma/theta per strike, depends on where that strike is withing the sigma ranges...
So that most definitely is based on probability. I don't know what else it can be based on...
What you're referring to is the change over time of that probability distribution... or the probabilities itself, which impacts IV.
Also, options on its own are a zero-sum game. The seller and buyer can't both make money.... one has to lose for the other to win. The only difference is when there's a hedge involved... but that changes the dynamics and that's a portfolio thing.
So that most definitely is based on probability. I don't know what else it can be based on...
What you're referring to is the change over time of that probability distribution... or the probabilities itself, which impacts IV.
Also, options on its own are a zero-sum game. The seller and buyer can't both make money.... one has to lose for the other to win. The only difference is when there's a hedge involved... but that changes the dynamics and that's a portfolio thing.
It's an implied probability, and doesn't imply direction. Assuming the market maker who sold me the OTM put has an adequately liquid market, he delta hedges and makes money, I go ITM and make money. So even if market maker is certain price will go up (and also certain of liquidity), he can profitably short and hedge a call. Price is constrained by arbitrage, not based on actual statistical probability of price movement (though they may, and likely do, coincide often).
Which circles back around to OP's point, if you can pick up one of these glitches in the matrix, you can exploit it indefinitely because a counter party can make money and will keep coming back to feed at the trough. The logic falls apart as you aggregate more data, but long option strategies (except straddles / strangles) depend on this holding true in selected cases.
Price is determined by the statistical probability of price movement by the input of volatility, and constrained by arbitrage, mainly put/call-parity.
I say input here... because contrary to the public believe that volatility is implied from the options price... it initially is used by the market makers etc to price the options. That's a fact.
So market makers use vol as a main input to price and quote you a market. They (delta)hedge all trades to basically only have a volatility position, based on the (near) future probability curve.
Roughly speaking, if that probability curve shifts... , bigger movements in all directions mean higher IV overall, move upwards expected due to say takeover/bid means higher vol in OTM calls/skew decrease to the puts, higher risks to downside means skew increase.
So probability in direction is usually shown in the skew....
Also, regarding this... I have to point out to the fact that, due to volatility being the main input of options prices... there most definitely will be a push in arbitrage to get options pricing in line with the current/forward expected volatility.
So technically you're correct in saying they need not reflect the actual statistical probability, that will be arbitraged away...
Also, what is the actual statistical probability? Who comes up with that? It's not historical, since that's in the past... and options pricing is forward. It's a bit current vol... but mainly the expected future/forward volatility (based on probabilities). The people buying and selling, the entire market, determines that. If there's not much interest in trading, so very illiquid products... then there is a higher chance of arbitrage. But then your guess is as good as the next one.
It doesn't exist, in that if you know actual "probability" it's a certainty. Language is a bit insufficient to capture the divergence between implied volatility and what I'm talking about. What I mean is given a set of circumstances on an individual stock, there can be a directional probability that cannot be reflected in option pricing, and I took this to the extreme with the example of being certain of price and direction.
I guess the best way to explain this is, suppose you know historically that a stock is more likely to go up than down, and an up move will be larger in magnitude than a down move...plus you're blessed with the knowledge this will hold true in the future. How do you price options as a market maker? In that scenario, calls carry more reward, so presumably more valuable to bring risk/reward into balance...but if I have the same knowledge as you as a spec buyer, guess where my orders come flowing in if you price options based on that probability.
Of course the counter argument is that the market has taken this into consideration to price for an even-odds scenario...And it's a perfectly legitimate point...but understanding where statistical models are likely to diverge from reality is a real and substantial edge.
You adjust the skew depending on the markets' expectations and risks.
When there's rumors regarding the takeover of a stock, you see either a more flat skewness or inverse. If the bid is know and the spot is roughly at the level of the bid... you will likely see a significant drop in IV and a high skew to the puts, since the risk is now that the takeover might fail and the target will drop 10-20% or whatever.
Same goes with bond options. Bonds tend to spike up on panics, the risks are to the upside so skew is inverted.
But also, when IV is already quite high because of a drop in value, either broad market or just a single stock... when the market starts to rise again you would see hard selling of OTM calls since the general idea is that IV is going to drop significantly. Of course this is hedged with either spot or ATM calls. Or spot + OTM puts... etc...
The IV curve/smile isn't fixed. It's adjusted on an ongoing basis. Whether probabilities line up with the actual outcome doesn't matter at the time, since we're all relying on trying to look into the future.
Historically, all stocks (the broad market) has always gone up more than down. Should skew generally be inverted? Does that mean that everyone should buy OTM calls? No... Statistically, you could say it's better to buy calls than puts, or even better to sell OTM puts... but you open yourself up to major risks.
If you would buy OTM calls, you've got time going against you in the form of theta.
If you would sell OTM puts, you've got time going for you... but a once in every x times event, like in February, would cause you serious problems.
If in this case you want to play the long game, just buy the spot... maybe even sell OTM calls and roll them over.
That's why skew to the puts exist. The market is nett-long and needs protection for downside through OTM puts. And because they are nett-long they can sell OTM calls on that position. That creates skew.
If you would buy OTM calls, you've got time going against you in the form of theta.
If you would sell OTM puts, you've got time going for you... but a once in every x times event, like in February, would cause you serious problems.
If in this case you want to play the long game, just buy the spot... maybe even sell OTM calls and roll them over.
That's why skew to the puts exist. The market is nett-long and needs protection for downside through OTM puts. And because they are nett-long they can sell OTM calls on that position. That creates skew.
@beerntrading you could look at those VIX ETFs that also have options on them. They drift....
Long VIX ETFs generally drift down because of the contango... so there's a big short interest in them. This causes a high short lending fee, which is reflected in the options pricing... basically the interest rate turns to negative for those, and in turn put/call-parity is affected. Skew is inverted.
Not sure about the inverse ETFs (drift upwards), I think the put/call parity would be normal... normal/steep skew I guess. Maybe not so steep... since overall IV would be fairly high.
Long VIX ETFs generally drift down because of the contango... so there's a big short interest in them. This causes a high short lending fee, which is reflected in the options pricing... basically the interest rate turns to negative for those, and in turn put/call-parity is affected. Skew is inverted.
Not sure about the inverse ETFs (drift upwards), I think the put/call parity would be normal... normal/steep skew I guess. Maybe not so steep... since overall IV would be fairly high.
Last edited: