I’m now confused as to what you mean by “real world” in this context?
Zvi is giving a credence for the event (p_zvi).
The market is offering a bet which implies some probability for the event (p_market).
All I am noting is p_zvi is different from p_market. I don’t think there’s anything special about the fact that options are involved here. (Unless I’m the one inferring you were specifically talking about options when you talk about “risk neutral measures”. All market probabilities are in some sense in risk neutral probabilities. If you’re complaint is about me talking about market probabilities then I guess this post wasn’t really for you?)
EDIT: To be more concrete about this, the places where “risk neutral” vs “real world” probabilities end up mattering is places where there is a concrete risk premium. (ie what the options market implies about stocks in 1y’s time doesn’t account for the fact that “stocks tend to go up over time”). In all the examples we’re talking about, those risk premiums are tiny relative to the numbers involved so they don’t make a significant difference to how we should be calculating the “market implied” odds.
Risk neutral pricing is always a danger when trying to make inferences about real world probabilities based on market pricing, but it’s usually a negligible one because participants in current prediction markets are generally speculators with no built-in exposure to the underlying asset, or ability to hedge against other markets.
On the other hand, implied probabilities from options pricing can differ significantly from real world probability, because any participant in the options market can hedge their position against the underlying asset.
“In all the examples we’re talking about, those risk premiums are tiny relative to the numbers involved so they don’t make a significant difference to how we should be calculating the “market implied” odds.” What evidence do you have that this is true? Your post is taking risk neutral probabilites from the market + your own opinion that risk neutral is similar to real world, then presenting that as the “market probability”, which is very misleading.
Edit: Maybe a better framing is that in order for option probabilities to give us a ~real world pdf of asset price at a given time, the asset needs to be approximately a martingale from now to the time in question. Many people would strongly disagree that BTC/ETH are even approximately a martingale on this time scale (they think there’s large positive drift). You are making a strong claim that is contrary to the view of many or most of the top crypto traders in the market, and yet you don’t make this clear but instead claim it’s a “market probability”, with the implication that people should defer to it unless they have strong domain knowledge.
because any participant in the options market can hedge their position against the underlying asset.
Right, but then the underlying asset is telling you something and if you disagree with that, then you can trade the underlying asset. There’s nothing special about options here. The difference comes from the fact that the underlying asset can have a return. (In the same way that a bond have a price different from par doesn’t (necessarily) mean that the market is forecasting default—they are discounting the value of a future cash flow).
What evidence do you have that this is true? Your post is taking risk neutral probabilites from the market + your own opinion that risk neutral is similar to real world, then presenting that as the “market probability”, which is very misleading.
The evidence would be something akin to “the historic sharpe for risk assets is <1” so the order magnitude of risk premia is “small enough” relative to the volatility.
I don’t think there is anything misleading about taking the market prices, constructing a bet and presenting that as a market probability, any more than taking showing betting odds and saying that’s the betting market probability. Sure, there might be some subtleties depending on the market (eg long-shot bias, fees, etc), but fundamentally that’s the price the market is offering. If you disagree, BET.
Edit: Maybe a better framing is that in order for option probabilities to give us a ~real world pdf of asset price at a given time, the asset needs to be approximately a martingale from now to the time in question. Many people would strongly disagree that BTC/ETH are even approximately a martingale on this time scale (they think there’s large positive drift).
I agree with this, all I’m saying is that the degree to which those assets fail to be a martingale is small relative to their volatility.
You are making a strong claim that is contrary to the view of many or most of the top crypto traders in the market, and yet you don’t make this clear but instead claim it’s a “market probability”, with the implication that people should defer to it unless they have strong domain knowledge.
I assume all those people are long crypto, which fundamentally means they disagree with the underling price and are long… I don’t see any inconsistency between that and what I’m saying. I would be more interested if you could find me someone who thinks both that
option prices are wrong
they shouldn’t have a position in options
they shouldn’t have a position in the underlying
because of some kind of risk-neutral vs real-world probability considerations.
I’m now confused as to what you mean by “real world” in this context?
Zvi is giving a credence for the event (p_zvi).
The market is offering a bet which implies some probability for the event (p_market).
All I am noting is p_zvi is different from p_market. I don’t think there’s anything special about the fact that options are involved here. (Unless I’m the one inferring you were specifically talking about options when you talk about “risk neutral measures”. All market probabilities are in some sense in risk neutral probabilities. If you’re complaint is about me talking about market probabilities then I guess this post wasn’t really for you?)
EDIT: To be more concrete about this, the places where “risk neutral” vs “real world” probabilities end up mattering is places where there is a concrete risk premium. (ie what the options market implies about stocks in 1y’s time doesn’t account for the fact that “stocks tend to go up over time”). In all the examples we’re talking about, those risk premiums are tiny relative to the numbers involved so they don’t make a significant difference to how we should be calculating the “market implied” odds.
Risk neutral pricing is always a danger when trying to make inferences about real world probabilities based on market pricing, but it’s usually a negligible one because participants in current prediction markets are generally speculators with no built-in exposure to the underlying asset, or ability to hedge against other markets.
On the other hand, implied probabilities from options pricing can differ significantly from real world probability, because any participant in the options market can hedge their position against the underlying asset.
“In all the examples we’re talking about, those risk premiums are tiny relative to the numbers involved so they don’t make a significant difference to how we should be calculating the “market implied” odds.” What evidence do you have that this is true? Your post is taking risk neutral probabilites from the market + your own opinion that risk neutral is similar to real world, then presenting that as the “market probability”, which is very misleading.
Edit: Maybe a better framing is that in order for option probabilities to give us a ~real world pdf of asset price at a given time, the asset needs to be approximately a martingale from now to the time in question. Many people would strongly disagree that BTC/ETH are even approximately a martingale on this time scale (they think there’s large positive drift). You are making a strong claim that is contrary to the view of many or most of the top crypto traders in the market, and yet you don’t make this clear but instead claim it’s a “market probability”, with the implication that people should defer to it unless they have strong domain knowledge.
Right, but then the underlying asset is telling you something and if you disagree with that, then you can trade the underlying asset. There’s nothing special about options here. The difference comes from the fact that the underlying asset can have a return. (In the same way that a bond have a price different from par doesn’t (necessarily) mean that the market is forecasting default—they are discounting the value of a future cash flow).
The evidence would be something akin to “the historic sharpe for risk assets is <1” so the order magnitude of risk premia is “small enough” relative to the volatility.
I don’t think there is anything misleading about taking the market prices, constructing a bet and presenting that as a market probability, any more than taking showing betting odds and saying that’s the betting market probability. Sure, there might be some subtleties depending on the market (eg long-shot bias, fees, etc), but fundamentally that’s the price the market is offering. If you disagree, BET.
I agree with this, all I’m saying is that the degree to which those assets fail to be a martingale is small relative to their volatility.
I assume all those people are long crypto, which fundamentally means they disagree with the underling price and are long… I don’t see any inconsistency between that and what I’m saying. I would be more interested if you could find me someone who thinks both that
option prices are wrong
they shouldn’t have a position in options
they shouldn’t have a position in the underlying
because of some kind of risk-neutral vs real-world probability considerations.