I want to say just âtrust the marketâ, but unfotunately, if OpenAI has a high but not astronomical valuation, then even if the market is right, that could mean âalmost certainly will be quite useful and profitable, chance of near-term AGI almost zeroâ or it could mean âprobably wonât be very useful or profitable at all, but 1 in 1000 chance of near-term AGI supports high valuation nonethelessâ or many things inbetween those two poles. So I guess we are sort of stuck with our own judgment?

For publically-traded US companies there are ways to figure out the variance of their future value, not just the mean, mostly by looking at option prices. Unfortunately, OpenAI isnât publically-traded and (afaik) has no liquid options market, but maybe other players (Nvidia? Microsoft?) can be more helpful there.

If you know how to do this, maybe itâd be useful to do it. (Maybe not though, Iâve never actually seen anyone defend âthe market assigns a non-negligible probability to an intelligence explosion.)

Itâs not really my specific area, but I had a quick look. (Frankly, this is mostly me just thinking out loud to see if I can come up with anything useful, and I donât promise that I succeed.)

Yahoo Finance has option prices with expirations in Dec 2026. Weâre mostly interested in upside potential rather than downside, so we look at call options, for which we see data up to strike prices of 280.[fn 1]

In principle I think the next step is to do something like invert Black-Scholes (perhaps (?) adjusting for the difference between European- and American-style options, assuming that these options are the latter), but that sounds hard, so letâs see if I can figure out something simpler from first principles:

The 280 strike Dec 2026 call option is the right to buy Nvidia stock, on Dec 18th 2026, for a price of $280. Nvidiaâs current price is ~$124, so these options only have value if the stock more than doubles by then. Theyâre currently trading at $14.50, while the 275 call trades at $15.

The value of a particular option is the integral of the optionâs payoff profile multiplied by the stock priceâs probability density. If we want something like âprobability the stock is at least X on date Yâ, the ideal option payoff profile would be an indicator function with a step at X, but we canât exactly get that. Instead, by buying a call struck at A and selling a call struck at B, we get a zero function up to A, then a linear increase from A to B, then a constant function from B. Picking A and B close together seems like the best approximation. It means looking at prices for very low-volume options, but looking at the nearby prices including for higher-volume options, they look superficially in line, so Iâll go with it.

More intuitively, if the stock was definitely going to be above both A and B, then the strike-A option would be BâA more valuable than the strike B option (that is, the right to buy a stock worth $10 for a price $1 is worth exactly $3 more than the right to do so for $4). If the stock was definitely going to be below both A and B, then both options would be worthless.

So the value of the two options differ by (BâA)P(the price is above B), plus some awkward term for when the price is between A and B, which you can hopefully make ignorable by making that interval small.

From this I hesitantly conclude that the options markets suggest that P(NVDA >= 280-ish) = 10%-ish?

[fn 1]: It looks like there are more strike prices than that, but all the ones after 280 I think arenât applicable: you can see a huge discontinuity in the prices from 280 to 290, and all the âlast trade dateâ fields for the higher options are from before mid-June, so I think these options donât exist anymore and come from before the 10-to-1 stock split.

I want to say just âtrust the marketâ, but unfotunately, if OpenAI has a high but not astronomical valuation, then even if the market is right, that could mean âalmost certainly will be quite useful and profitable, chance of near-term AGI almost zeroâ or it could mean âprobably wonât be very useful or profitable at all, but 1 in 1000 chance of near-term AGI supports high valuation nonethelessâ or many things inbetween those two poles. So I guess we are sort of stuck with our own judgment?

For publically-traded US companies there are ways to figure out the variance of their future value, not just the mean, mostly by looking at option prices. Unfortunately, OpenAI isnât publically-traded and (afaik) has no liquid options market, but maybe other players (Nvidia? Microsoft?) can be more helpful there.

If you know how to do this, maybe itâd be useful to do it. (Maybe not though, Iâve never actually seen anyone defend âthe market assigns a non-negligible probability to an intelligence explosion.)

Itâs not really my specific area, but I had a quick look. (Frankly, this is mostly me just thinking out loud to see if I can come up with anything useful, and I donât promise that I succeed.)

Yahoo Finance has option prices with expirations in Dec 2026. Weâre mostly interested in upside potential rather than downside, so we look at call options, for which we see data up to strike prices of 280.[fn 1]

In principle I think the next step is to do something like invert Black-Scholes (perhaps (?) adjusting for the difference between European- and American-style options, assuming that these options are the latter), but that sounds hard, so letâs see if I can figure out something simpler from first principles:

The 280 strike Dec 2026 call option is the right to buy Nvidia stock, on Dec 18th 2026, for a price of $280. Nvidiaâs current price is ~$124, so these options only have value if the stock more than doubles by then. Theyâre currently trading at $14.50, while the 275 call trades at $15.

The value of a particular option is the integral of the optionâs payoff profile multiplied by the stock priceâs probability density. If we want something like âprobability the stock is at least X on date Yâ, the ideal option payoff profile would be an indicator function with a step at X, but we canât exactly get that. Instead, by buying a call struck at A and selling a call struck at B, we get a zero function up to A, then a linear increase from A to B, then a constant function from B. Picking A and B close together seems like the best approximation. It means looking at prices for very low-volume options, but looking at the nearby prices including for higher-volume options, they look superficially in line, so Iâll go with it.

More intuitively, if the stock was definitely going to be above both A and B, then the strike-A option would be BâA more valuable than the strike B option (that is, the right to buy a stock worth $10 for a price $1 is worth exactly $3 more than the right to do so for $4). If the stock was definitely going to be below both A and B, then both options would be worthless.

So the value of the two options differ by (BâA)P(the price is above B), plus some awkward term for when the price is between A and B, which you can hopefully make ignorable by making that interval small.

From this I hesitantly conclude that the options markets suggest that P(NVDA >= 280-ish) = 10%-ish?

[fn 1]: It looks like there are more strike prices than that, but all the ones after 280 I think arenât applicable: you can see a huge discontinuity in the prices from 280 to 290, and all the âlast trade dateâ fields for the higher options are from before mid-June, so I think these options donât exist anymore and come from before the 10-to-1 stock split.