I think the author has confused one type of payoff diagram (the probability density function of a variable) with another (the payoff of an option plotted against the value of the underlying variable). This results in a number of the claims in the piece being reversed. There seems to be confusion between other parameters too.

In finance, an option is the right to do something (typically some variant of 'buy asset A for price P'). The most surprising thing is that the piece doesn't establish where the optionality comes from. I think it just draws an analogy between the distribution of future outcomes and the payoff of an option, then treats the value of the future like an option. As above, I think this is incorrect.

One way the conclusions would carry is if one asserts that the future is net positive in expectation largely independently of size, and thus one should make the future bigger (a particular version of more variance). This argument is coherent but does not involve options.

A plausible source of optionality is that future generations might have some control over whether the world continues.* (Finance jargon would call this a put option on the future of the world with a low strike.)

Under this interpretation:

• Standard options pricing theory applies when you can trade the thing you have an option on. Here that isn't the case: one cannot buy and sell the future to hedge the option delta.
• One should instead use more straightforward expected utility calculations taking into account the expected actions of future actors. e.g. a crude simplification: P(world good)×(how good)×P( future actors let world continue | good) - P(world bad)×(how bad)×P(future actors let world continue | bad). Standard financial options pricing would give a very different formula.
• The volatility point does hold, but for the above reasons, not the analogy drawn in the piece. One should simply be willing to trade extra potential upside (before future generations intervene) for extra potential downside (before intervention) in proportion to how much future generations have the power to stop bad outcomes closer to the time.
• The claim that we are long a call and short a put seems false -- I think this is just drawing an incorrect analogy as noted in the first paragraph. I think the situation is more like owning an X% put on the future, where X% is the chance that future altruists have control over whether the long-term future exists. (You could alternatively see the overall situation as long X calls and long (1-X) futures.) This weakens but does not nullify the amount that a balanced upside and downside leads to focusing more on the present.

*Seems unclear but worth considering.

In conclusion, I got some interesting thinking out of reading this piece, but disagree with most of it.

I don't know enough about options it seems for this to feel like it's giving me a useful additional way to think about moral weight of future patients relative to present ones, but I expect if I did know enough about them this would feel like a useful model to employ intuitions about options to explain an issue in ethics, similar to the way preference theory is often useful for helping to make sense of some questions related to values.