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As an active participant on the Physics Stack Exchange I have, on several separate occasions, run into some vague remarks about the 'intimate relation' between the famous Black-Scholes model in economics and the Schrödinger equation that appears in quantum mechanics. In particular, people mention that path integrals (a certain technique that is very useful in quantum mechanical calculations) find many applications in economic settings.

I'd love if someone could make this connection clearer by

  • Explicitly (i.e. in equations) showing how the Schrödinger equation and the Black-Scholes equation are related

  • Discussing the use of path integrals in economics

Danu
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  • P.S. Please feel free to add (or remove) tags; I'm not an expert in economics. – Danu Nov 18 '14 at 21:27
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    Wouldn't this be a better fit for Quantitative Finance? – Steve S Nov 18 '14 at 21:31
  • @SteveS would this not fall in the category economics? Curious... – Danu Nov 18 '14 at 21:33
  • Well, to the extent that Quantitative Finance is a subset of Economics, sure. (Frankly, I've always wondered why "Quantitative Finance" came before "Economics" anyway). It's just that my initial impulse was that, well, it'd fit in better over at a more-narrowly focused site like the Quant StackExchange. – Steve S Nov 18 '14 at 22:16
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    I agree with Steve. The Black-Scholes is very related to quantitative financing, which is only one small portion of economics as a whole. – Nate Vomocil Nov 18 '14 at 22:30
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    @NateVomocil I'm still not sure that this should make it off-topic here. Could someone provide a reference to better understand what this SE is intended for? – Danu Nov 18 '14 at 22:37
  • @Danu: It's not that it's off-topic, per se--just that I think it's more on-topic over at Quant SE (if that makes sense). – Steve S Nov 18 '14 at 23:13
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    @SteveS I wonder if we might benefit from a meta discussion as to whether we should avoid poaching questions that can go on specific sub-discipline stacks? :-) – LateralFractal Nov 19 '14 at 02:21
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    This question appears to be off-topic because pertains much more to quantitative finance than economics. – daOnlyBG Nov 19 '14 at 09:13
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    @daOnlyBG that doesn't make it off-topic. It's a valid economics question. The fact that it could be on-topic at another site doesn't make it off-topic here at all. Whether it's answerable, and whether it's an appropriate expert question, is a different matter: but just being valid on more than one SE site is not a sufficient reason to close or to migrate. – 410 gone Nov 19 '14 at 14:02

1 Answers1

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I have more often heard of how the Black-Scholes equation is just the heat equation. You can find that information here. I haven't heard of a relationship between Black-Scholes and quantum mechanics before, but this post on the Physics stack exchange seems to have the details you're looking for. (Maybe you've seen this post before.)

Community
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jmbejara
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  • Yes, the Black-Scholes differential equation can be transformed into the heat equation by a change of variables. – Geremia Feb 05 '18 at 21:37
  • Well, the Schrodinger equation is the complex analysis equivalent of the heat equation so the relationship seems legit. – P. C. Spaniel Mar 27 '18 at 18:26