Calculate Fair Implied vol

Im trying to calculate fair value for KO Ivol given the following information.

PEP/USD Ivol = 30%
PEP/KO Ivol = 9%
PEP/USD and KO/USD Implied Correlation is 80%

Im sure its a very basic formula, but i am not able to figure it out.

Thank you

 

What have Pepsi and CocaCola to do with the ProShares Ultra Semiconductors (USD) ETF?
Or do you rather mean the US Dollar? Hmm. wouldn't make any sense, IMO.

Or are these not the beverage companies but some currencies maybe, or something else?

Take a look at the formulas in this paper / article:
https://www.rebellionresearch.com/implied-correlation
https://www.aeaweb.org/conference/2018/preliminary/paper/Rt6FbZde

 

SL priced these for a living.

 

PEP/ KO Implied = 9%??
I must be missing something ..

Pep vol divided by KO vol = 9 percent or 90%??

 

If you create an asset of KO/USD over PEP/USD you create KO/PEP. And if you take the vol of that let’s say it’s 9%.
Think of the KO/PEP similar to a uniswap BTC/ETH pool

 

Gotcha..So it's an outperformance option and Ivol of Pep/Ko is actually historical vol of the ratio?

 

Yes the 9% is the ivol of the ratio.
Do you happen to know the answer to the original question - given the data provided could you price fair for KO/USD option?

 

The what and why's are above my head at the moment, but that is how I learn sometime... one day I will understand more.

Out of curiosity I copied your question into chatgpt and I got this:

chatgpt:
To calculate the fair value implied volatility for KO (The Coca-Cola Company) given the provided information, you can use the concept of implied correlation and relative implied volatility. Here's the formula:

KO Ivol = PEP/USD Ivol * (PEP/KO Ivol) / (PEP/USD and KO/USD Implied Correlation)

Let's plug in the values given:

KO Ivol = 30% * (9%) / (80%)
KO Ivol = 0.3375 or 33.75%

Therefore, based on the provided information, the fair value implied volatility for KO would be approximately 33.75%.

Please note that this calculation assumes that the implied correlation and relative implied volatility remain constant and that other factors influencing option prices are negligible. It's important to consider this as a basic estimation, and market conditions may vary.
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never know it helps, as you mentioned that you expected it to be simple.

I can go back to decipher the "what and why" now...

 

What is the purpose? Using the Correlation as a signal that something is off with the implied volatility in KO or PEP? If it's the latter wouldn't you be able to scan for it directly?

 

.234

> sqrt(.3**2 + .09**2 - 2 * .3 * .09 * .8)
[1] 0.2343075

Law of cosines:

c^2 = a^2 + b^2 - 2 * a * b * rho

rho = correlation(a,b) = cosine(a,b)

Also you can look at it geometrically: You are looking for the KO/USD vector's point of tangency with the .09 radius circle centered at the end of the PEP/USD vector. Remember that Jim Simons once implied that all the great market mathematicians were, like himself, geometors.

It's all in Wystrup.