Creating a Ratio Option

L

legacyvbc

I need help on determining the correct implied volatility for a synthetic option I am trying to create (as a test).

I will use MSFT and the QQQQ as an example. I want to price an option on the ratio of MSFT to the QQQQ.

The current ratio is .6884 and has ranged from .7498 to .5535 over the past year. Obviously I can price an option using the BS model and the historical volatility of the spread but I am trying to figure out what the implied vol should be based on the MSFT implied and the QQQQ implied.

Lets say I am looking at the Jan-09 options which shows the following implied vols for the ATM calls: MSFT Jan 20's are ~60 and QQQQ Jan 30's are 52.91.

Does that mean I should be using the current price ratio for the implied?

Any help is greatly appreciated.

Thanks
 
I'm sure someone more educated in exotics than me will voice their opinion on this, but my guess is that you can't just use the ratio of IVs as you need to take into account the correlation as well.

I guess it is similar to a dispersion trade, where, as far as I know, correlation plays an important role.
 
Quote from legacyvbc:

I need help on determining the correct implied volatility for a synthetic option I am trying to create (as a test).

I will use MSFT and the QQQQ as an example. I want to price an option on the ratio of MSFT to the QQQQ.

The current ratio is .6884 and has ranged from .7498 to .5535 over the past year. Obviously I can price an option using the BS model and the historical volatility of the spread but I am trying to figure out what the implied vol should be based on the MSFT implied and the QQQQ implied.

Lets say I am looking at the Jan-09 options which shows the following implied vols for the ATM calls: MSFT Jan 20's are ~60 and QQQQ Jan 30's are 52.91.

Does that mean I should be using the current price ratio for the implied?

Any help is greatly appreciated.

Thanks
More...

I don't have a pat answer for you, but here are some thoughts.

To guide your ratio, I think what you want is the following:

(delta of QQQQ options) x (dollar value of QQQQ) = -(delta of MSFT options) x (dollar value of MSFT)

In other words, if QQQQ shares are 29 and MSFT shares are 19, and all your options have a delta of .5, then you could be long 19 QQQQ calls and short 29 MSFT calls, because 19 x $2900 x .5 = 27,550, and 29 x $1900 x .5 also = 27,550. So your QQQQ option position has the same "dollar delta" as your MSFT position. That should make the ratio play work.

But it would seem to me that you need two things to be in place in order for this play to work:

1. The QQQQ/MSFT ratio has to be at its historic extreme (which you've already figured out)

But also -

2. The spread between the IV of QQQQ and IV of MSFT also should be somewhat "stretched" based on their historical relationship. At the very least, you don't want them to be out of line the "wrong way" relative to their historical relationship.

As for number 2., I think you're looking at absolute spread rather than ratio. That assumes that their vegas are approximately equal. Off the top of my head I think they should be, but check for yourself to see if that's true.
 
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