
I am trying to find a good practical example of Bayes' theorem use in finance. I have a great example in medicine with cancer screening, but I struggle to find something cool in finance. Should be simple enough for undergraduate students, does anyone have any ideas?

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nikol


Total Posts: 803 
Joined: Jun 2005 


Risk management problem:
P(account of clientA is in limit breach)*P(history of limit breachesclients defaulted)=>P(clientA is in default)
Trading problem:
P(see uptick)*P(history of upticks  uptrends)=>P(beginning of uptrend)
PS: My mistake. Above should be modified from 'beginning updtrend' to 'uptrend'. Correct is this: P(see uptick)*P(history of upticks  start of uptrends)=>P(we are at beginning of uptrend)




goldorak


Total Posts: 1062 
Joined: Nov 2004 


We are in 2019 and finance folks are still relying on frequentist statistics. That tells a lot about this industry.
Once you actually reverse the way we have been (wrongly) trained to look at things in finance, and consider the probability of the hypothesis you make given the data you observe rather than the probability of the data given the hypothesis you make, the use of Baye's theorem is pretty straightforward.

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bullero


Total Posts: 57 
Joined: Feb 2018 


Parameter estimation?
Edit: For example in stat arb you could sample the posterior joint distribution for a set of interesting parameters that describe the stochastic behavior of a spread you are trading. Then, given the joint density you compute the expected pnl. 



AB12358


Total Posts: 63 
Joined: Apr 2014 

 


@goldorak, we have:
P(HD)=P(DH)*P(H)/P(D)
So in order to get the probability of the hypothesis (H) given the data (D), we need unconditional probabilities of the data and hypothesis... How do we go about those?
I know you are super clever, please explain like I am 12 years old. 
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Maggette


Total Posts: 1157 
Joined: Jun 2007 


Sorry, I guess I am missing something here. I don't get the question. You are aware of the classical Bayesian inference stuff (start with a prior for the parameters ...posterion = prior * likelihood..etc)?
In general you don't do that in a closed form pen and paper way....
Edit: I get know that I misunderstood the question. I guess you are looking for a more direct application of the theorem, other than general bayesian statistics 
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nikol


Total Posts: 803 
Joined: Jun 2005 


@NeroTulip
>> P(HD)=P(DH)*P(H)/P(D)
Usually P(D) = 1.
>> I know you are super clever, please explain like I am 12 years old.
Hm... Assume that you already explained the concept of probability.
Imagine walking in the museum and seeing Kandinsky's Composition no.XI https://www.wassilykandinsky.org/YellowRedBlue.jsp
Data is painting H is everything what tells imagination about the picture. P(H) is a probability that particular H (let say face) will appear among anything else. P(DH) is a number (EDIT: better fraction=P(DH)/P(D)) of paintings with faces on it. Portraits included.
Then P(HD) is a probability that what I see is face indeed.




vertigo


Total Posts: 5 
Joined: Dec 2015 


Regarding Goldorak's post... I think this kind of thinking is worse than useless  it is dangerous. Young people will look at your post and take inspiration, and then get a harsh reality shock when they attempt to use Bayesian methods in practice and found out that these methods are more complicated, more difficult to calibrate and far more subjective than frequentist methods. In my opinion, they are nearly useless in finance.
It is not that finance folks "believe" on frequentist statistics, no, that is how an academic would see it (and academic's opinions count as the same as garbage cleaners)  more likely it is that they are aware of the dangers of using more complicated statistical methods (i.e., Bayesian methods) and therefore use more simple methods that have damage limitations.
You cannot use Bayesian methods for pricing  when you work with the martingale measure, the volatility function is already specified, and the drift is whatever rate you can finance with (LIBOR, OIS, etc...). You could use Bayesian methods for risk  but usually "risk models" need to get regulatory approval and you tend to use simple models (i.e., not subjective) for such cases. Therefore, Bayesian methods are useless.
An example of where you could use them  calibration for yield curves. 
... maybe one day ... 




To Bayes or not to Bayes, that is the question. (ok, kill me now)
@Maggette: Indeed, I am looking for an example of simple direct application of Bayes' theorem in finance, something I could explain to some undergrads.
For example, in medicine, you want to know the probability that you have cancer given that your screening test is positive P(CT). You know the test sensitivity P(TC), the false positive rate P(Tnot(C)), and the prevalence in the general population P(C). Direct application of the theorem gives you the result you are looking for, which can be counterintuitive e.g. your test is positive, but you only have a 15% chance of actually having cancer.
Wondering if there are simple examples like that in finance.

"Earth: some bacteria and basic life forms, no sign of intelligent life" (Message from a type III civilization probe sent to the solar system circa 2016) 

