Sure thing. :)
This interference creates a very different probability distribution for the asset’s final price to that generated by the classical model. The bell curve is replaced by a series of peaks and troughs.
-- No, it's not replaced by "a series of peaks and troughs". This is nonsense. It sounds flashy, as it reminds of the peaks and troughs seen in the double-slit experiment, but it does not accurately describe what could be done to improve modeling with probability distributions. Looking at it from an information-theoretic point of view, peaks and troughs in a probability density distribution would just mean lower entropy, i.e. it would be implicitly assumed to contain (quite a lot) more specific information than another, smoother PDF. So where does this information suddenly come from?? If this is not what the author meant, then it is at least an unfavorable choice of wording to write that "the bell curve is replaced by a series of peaks and troughs". To have mercy on the author, one could maybe assume they meant to speak about a characteristic function (https://en.wikipedia.org/wiki/Characteristic_function_(proba...) but that does not seem to be the case.
Furthermore, any probability distribution may be used to model financial instruments, depending on how well it appears to be suited for the purpose of modeling reality. However, if the author already speaks about it so specifically, it is almost misleading not to mention that normal distributions (the bell curve) are in practice not used in the way described, at least not by people who know what they are doing. Consider why Nassim Nicholas Taleb (author of "Fooled by Randomness" and "Black Swan") said that no one in the industry uses Black-Scholes, or ever has. What he was referring to - correctly - is that (in the options space) nobody uses the normal distribution assumption to be correct for the modeling of asset prices per se. It is rather used as a stepping stone with some convenient mathematical properties to describe things analytically.
Broadly speaking, the classical random walk is a better description of how asset prices move. But the quantum walk better explains how investors think about their movements when buying call options [...]
-- Nonsense. There is not even a hint of an explanation why either of the two would be so. It is merely an empty sentence that reads well. Quantum walk explains investor rationale and psychology? And only when buying call options?! This is quite funny actually.
A call option is generally much cheaper than its underlying asset, but gives a big pay-off if the asset’s price jumps.
-- Not always so. It depends on many things. Calls actually consistently disappoint some buyers by moving much less on the way up than what they expected / had hoped for. Having looked at a call's delta as per Black-Scholes, they end up wondering why the call did not move as much as the delta would have predicted. It has to do with spot-vol correlation (and other things), but I won't go down this rabbit hole now... (I would say you can PM me if you are truly interested and want to know more, but it does not seem to be possible on HN.)
The scenarios foremost in the buyer’s mind are not a gentle drift in the price but a large move up (from which they want to benefit) or a big drop (to which they want to limit their exposure).
-- If you are a buyer of a call option you would certainly not hope for a big drop in the underlying (!) and neither would you limit your exposure to such event by buying a call. This is, unless you hedged it either delta-flat or fully, which essentially transforms the call into a synthetic put. Nothing of that sort is mentioned here.
The prices of such options closely match those predicted by an algorithm based on the classical random walk (in part because that is the model most traders accept).
-- No, they do not match a price "predicted" by an algorithm (assuming the author is referring to market prices of the options here). It is the other way around. The assumptions ultimately used to make the algorithm fit the market are what is "predicted" by the market. The "algorithm" referred to here is likely the Black-Scholes formula and it does not predict any market prices. It gives you an idea where the expected value of the option would be if all of its unrealistic assumptions were true (which they aren't). So you have a function with many parameters, one of the most important ones in this context being implied future volatility (average future variance to be super-correct). But you still have to make a choice of what such inputs you want to use for them (the formula will spit out almost anything for the right choice of inputs). In practice, a subset of these parameters differs for each option from strike to strike, so there is no "close" match found to market prices at all.
But a quantum walk, by assigning such options a higher value than the classical model, explains buyers’ preference for them.
-- No. Rubbish. How is this comparison even made. Assigning a higher value, based on what benchmark or standard of comparison? The same input parameters to the pricing model? Hardly, as a quantum model would likely have quite different parameters than a "classical" one. This is just textual fluff.
Such ideas may still sound abstract. But they will soon be physically embodied on trading floors, whether the theory is adopted or not. Quantum computers, which replace the usual zeros and ones with superpositions of the two, are nearing commercial viability and promise faster calculations. Any bank wishing to retain its edge will need to embrace them. Their hardware, meanwhile, makes running quantum-walk models easier than classical ones. One way or another, finance will catch up.
-- Hype paragraph.