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goranrf


Total Posts: 2
Joined: Oct 2016
 
Posted: 2016-10-27 16:46
Let's assume company A has a market cap of 2, and company B of 1.
The implied volatility of the company A is 15, and of B is 20.
Their historical correlation is 0,3.
If company the company A buys the company B, how would you calculate the "basket" implied volatility of the new company A+B? (Using the weights 67% and 33%, the volatilities prior to the acquisition, and the pre-announcement historical correlation)

fomisha


Total Posts: 20
Joined: Jul 2007
 
Posted: 2016-10-27 17:41
A good starting point could be taking the implied vol curve of A and rescaling it by the ratio of the realized vol of the basket over the realized of A. Obviously, one needs to throw out the points related to the announcements. Then you can think of how the flows will affect the vol short term after the merger and how the company restructuring will affect the vol long term.

chiral3
Founding Member

Total Posts: 4974
Joined: Mar 2004
 
Posted: 2016-10-27 20:30
I am going to guess the actual answer is not 17.98%

Nonius is Satoshi Nakamoto. 物の哀れ

deeds


Total Posts: 341
Joined: Dec 2008
 
Posted: 2016-10-28 01:41

Avellaneda, Reconstructing Volatility, may be relevant

https://www.math.nyu.edu/faculty/avellane/Avellaneda.pdf

baghead


Total Posts: 861
Joined: Sep 2004
 
Posted: 2016-10-28 12:26
First of all, you need to decide if the basket approach is the right one which I doubt. And here is why-

the two companies will stay listed individually for the time between announcement and closing of the deal.
The stock prices will converge based on the economics of the deal, the likelihood of closing and the impact on the combined balance sheet. So will vols.

If it's an all shares 2:1 deal vols will look different to an 1,5:1 + $X or an all cash deal. If it's the latter, company B's vol will drop to almost zero until the deal goes through and its shares are delisted while company A's vol is likely to rise as there are more volatile assets on the balance sheet compared to the initial cash. Or the new assets actually fit the book and decrease risk (vertical integration, for example)

In an all shares deal, vols might converge to the basket. Or the market decides that NewCo is either more or less than the sum of its parts. who knows....


deeds


Total Posts: 341
Joined: Dec 2008
 
Posted: 2016-10-28 13:19

@baghead,

- dynamic aspect is tough but perhaps some reasonably broad assumptions or approximation like interval (avellenada vol uncertainty) or average (black scholes robustness) eases us back into a simple framework given reasonably short time course of deal? (nothing can be done about the non-financial event driven regime changes, capital structure changes, except to track with properly updated subjective or risk neutralized probabilities)

- wrt to form of deal, share exchange, etc...if basket summary is deemed appropriate for purpose of model, could some initial assumptions be made given current information which captures compound option contribution to associated summary volatility or delta/gamma/vega apx? These updated 'properly' as information comes in?

Seems a key question is which uncertainties to summarize in a risk parameter, which to break out into subjective probability or scenario.

pj


Total Posts: 3305
Joined: Jun 2004
 
Posted: 2016-10-28 13:56
Gentlemen,
aren't you over-complicating a simple homework problem?

I saw a dead fish on the pavement and thought 'what did you expect? There's no water 'round here stupid, shoulda stayed where it was wet.'

EspressoLover


Total Posts: 205
Joined: Jan 2015
 
Posted: 2016-10-28 23:19
I'd say that even the framework of how you're approach the problem is incomplete. Especially at short-tenors, a significant proportion of volatility is driven by noise trading. The corporate structure itself is probably insufficient to determine how the new entity behaves. You also have to take into consideration the buy-side.

Even more succinctly, I'd be willing to bet money that under the exact same merger terms, the new entity's volatility behaves a lot more like A if it keeps A's ticker. And more like B if it uses B's ticker.

goranrf


Total Posts: 2
Joined: Oct 2016
 
Posted: 2016-11-03 10:32
I was looking more towards a simple solution. To redefine my question, how would you calculate the implied vola of a basket of 2 stocks, with the weights a and b and a realised correlation of c.

ronin


Total Posts: 172
Joined: May 2006
 
Posted: 2016-11-03 11:45
>I was looking more towards a simple solution. To redefine my question, how would you calculate the implied vola of a basket of 2 stocks, with the weights a and b and a realised correlation of c.


OMG, this is wonderful. @goranrf 1 : nuclearphynance 0.



"People say nothing's impossible, but I do nothing every day" --Winnie The Pooh

HitmanH


Total Posts: 413
Joined: Apr 2005
 
Posted: 2016-11-03 11:47
Homework for sure!
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