<p>I have more often heard of how the Black-Scholes equation is just the heat equation. You can find that information <a href="https://quant.stackexchange.com/questions/84/transformation-from-the-black-scholes-differential-equation-to-the-diffusion-equ">here</a>. I haven't heard of a relationship between Black-Scholes and quantum mechanics before, but <a href="https://physics.stackexchange.com/questions/60242/relation-between-black-scholes-equation-and-quantum-mechanics">this</a> post on the Physics stack exchange seems to have the details you're looking for. (Maybe you've seen this post before.)</p>

CC BY-SA 3.0
2018-02-05T21:37:08.317Z
Yes, the Black-Scholes differential equation can be transformed into the heat equation by a change of variables.
Geremia
CC BY-SA 3.0
2018-03-27T18:26:04.037Z
Well, the Schrodinger equation is the complex analysis equivalent of the heat equation so the relationship seems legit.
P. C. Spaniel
CC BY-SA 3.0
2014-11-19T01:06:42.327Z
2014-11-19T01:06:42.327Z
2017-04-13T12:46:23.963Z
jmbejara
<p>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 <em>path integrals</em> (a certain technique that is very useful in quantum mechanical calculations) find many applications in economic settings. </p>

<p>I'd love if someone could make this connection clearer by </p>

<ul>
<li><p>Explicitly (i.e. in equations) showing how the Schrödinger equation and the Black-Scholes equation are related</p></li>
<li><p>Discussing the use of path integrals in economics</p></li>
</ul>

CC BY-SA 3.0
2014-11-18T21:27:13.627Z
P.S. Please feel free to add (or remove) tags; I'm not an expert in economics.
Danu
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2014-11-18T21:31:54.870Z
Wouldn't this be a better fit for [Quantitative Finance](http://quant.stackexchange.com/)?
Steve S
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2014-11-18T21:33:01.893Z
@SteveS would this not fall in the category *economics*? Curious...
Danu
CC BY-SA 3.0
2014-11-18T22:16:46.343Z
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
CC BY-SA 3.0
2014-11-18T22:30:29.297Z
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
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2014-11-18T22:37:38.467Z
@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
CC BY-SA 3.0
2014-11-18T23:13:26.543Z
@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
CC BY-SA 3.0
2014-11-19T02:21:26.617Z
@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
CC BY-SA 3.0
2014-11-19T09:13:30.783Z
This question appears to be off-topic because pertains much more to quantitative finance than economics.
daOnlyBG
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2014-11-19T14:02:47.390Z
@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
<black-scholes-model><interdisciplinary><mathematical-economics>
The relation between the Black-Scholes model and quantum mechanics
Danu
# The relation between the Black-Scholes model and quantum mechanics

(Asked by: username_0 on 2014-11-18)

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

**Tags:** black-scholes-model, interdisciplinary, mathematical-economics

> **Comments:**
> **username_0**: P.S. Please feel free to add (or remove) tags; I'm not an expert in economics.  
> **username_1**: Wouldn't this be a better fit for [Quantitative Finance](http://quant.stackexchange.com/)?  
> **username_0**: @SteveS would this not fall in the category *economics*? Curious...  
> **username_1**: 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.  
> **username_2**: I agree with Steve. The Black-Scholes is very related to quantitative financing, which is only one small portion of economics as a whole.  
> **username_0**: @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?  
> **username_1**: @username_0: 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).  
> **username_3**: @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? :-)  
> **username_4**: This question appears to be off-topic because pertains much more to quantitative finance than economics.  
> **username_5**: @username_4 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.  

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## 1 answers

### Answer by username_6 on 2014-11-19. Score: 1

I have more often heard of how the Black-Scholes equation is just the heat equation. You can find that information [here](https://quant.stackexchange.com/questions/84/transformation-from-the-black-scholes-differential-equation-to-the-diffusion-equ). I haven't heard of a relationship between Black-Scholes and quantum mechanics before, but [this](https://physics.stackexchange.com/questions/60242/relation-between-black-scholes-equation-and-quantum-mechanics) post on the Physics stack exchange seems to have the details you're looking for. (Maybe you've seen this post before.)

> **Comments:**
> **username_7**: Yes, the Black-Scholes differential equation can be transformed into the heat equation by a change of variables.  
> **username_8**: Well, the Schrodinger equation is the complex analysis equivalent of the heat equation so the relationship seems legit.  

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