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mathdude2018
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Posts: 8
Joined: January 10th, 2018, 4:35 pm

Volatility of B from correlation with another asset A

November 7th, 2019, 2:03 pm

I have two assets A and B. 

I know the correlation of A and B and I also know the volatility of A. 

Is it possible to generate the volatility of B? If not, why?
 
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tw
Posts: 1073
Joined: May 10th, 2002, 3:30 pm

Re: Volatility of B from correlation with another asset A

November 7th, 2019, 2:59 pm

I have two assets A and B. 

I know the correlation of A and B and I also know the volatility of A. 

Is it possible to generate the volatility of B? If not, why?
No. 

Correlation is a measure (in some sense) of how frequently A and B move in the same direction.
Volatility says how far they move.  
 
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DavidJN
Posts: 1738
Joined: July 14th, 2002, 3:00 am

Re: Volatility of B from correlation with another asset A

November 7th, 2019, 5:50 pm

A concrete example of your problem faced frequently by middle offices would be the following - you have two traded assets so they both have a historical price and return history. One asset has liquid options traded on it but the other has none. Your front office wants to trade an option on the asset without any option activity and uyou have to derive some way of marking it.

There are a variety of ways to create a proxy for this situation. A simple one is to multiply the implied volatility of the asset with traded options by the ratio of the historical return standard deviations. Other techniques involve using regression and the like. You might be able to get some ideas for creating proxies in such situations by researching what related functionality the market data vendor platforms offer (e.g. Markit, Neoxam, SAS, etc.). I have no affiliation with any of those companies for the record. The search key words are "proxy creation" and IPV (independent price verification).
 
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katastrofa
Posts: 8376
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri

Re: Volatility of B from correlation with another asset A

November 8th, 2019, 12:29 am

If you had covariance, you could estimate bounds on the volatility: Vol(B) <= |Cov(A,B)| / Vol(A). Otherwise, you could try to analyse the problem at the level of the equations of Brownian motion: think what values of their parameters yield the information you have, and in turn what volatility in question they might (or mightn't) produce.
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