Figuring out IV of a portfolio of options

T

TskTsk

Say you buy a bear put spread by buying a PUT @25D and selling a PUT @10D. The 25D has an IV of 14% and the 10D has an IV of 18%. Say you then deltahedge this, and at expiry you've realized 10% volatility. Then what is your loss? Loss is IV you bought at minus your realized vol but what IV did you buy at ? What is the portfolio IV of the above position?

The way I figure out the portfolio IV is by looking at theta divided by gamma of the portfolio, then compare to an option with the exact same theta/gamma ratio and look at it's IV. Then that options IV is equal to the portfolio IV. Can you do it this way or is there some other way?
 
Well, taking theta-gamma equivalent option is a nice idea, but what would you do for a calendar spread? :)

On a serious note, once you introduce more then a single option, you need to do fancier analysis to account for possible path dependency.
 
Probably backing out IV isn't even neccessary for comparison, the theta/gamma value I think can be used alone and to me at least it's more inituitive than IV. Also plotting it (for single options accross the term structure) in a 3d-chart it looks similar to the IV term structure. I tried plotting 3d-chart of structures as well, for instance bull put spreads, but again I'm unsure if it has any value. Wish it does because I hate fancy analysis, I'll take back of the envelope math any day of the week :) For instance for the 1:1 25d-10d bull put spread on SPX Dec'13 I backed out a vol of 9.5 or so vs. ATM vol of 11. (This was earlier today). I believe it's because of the extreme skew in near-month causing the long-option to be too expensive, as this difference is less going further out...But again not sure if it has any value.
 
I've thought of something, say you want to exploit what you think is high skew, isn't it possible to just sell a straddle (or any structure, vertical, whatever, anywhere on the chain) asses it's theta/gamma ratio, then instead of hedging it with it's real theta/gamma ratio, hedge it with a theta/gamma ratio that is equivalent to that of a 25D put option? (essentially hedging with lower gamma than the actual, but with same theta). It's a way to sell "skew premium", but get way better margin treatment vs. selling the pure short 25D put option and hedging it. Besides the erratic P&L of hedging against expected RV instead of IV, and the need to hedge it until expiry, I cannot for the life of me figure out what's wrong with this. Any input?
 
You aren't monetizing the skew as much as expressing the view that the straddle should be priced at the same vol as the 25 delta put.

The goal of delta hedging is to hedge to the actual realized vol. That will reduce your pnl volatility the most.



Trading short skew is very tricky. Lots of third order and path dependency effects. That attractive gamma/theta profile is really the hidden costs of those effects.
 
Thanks for the input

Essentially my above point is that you hedge whatever premium you receive in a way that within expiry, gives you the exact same PnL you would expect from selling the premium at the 25D put instead. Because the 25D put has a more favorable theta/gamma ratio, hedging your premium against this ratio should be the same as actually selling the 25D put premium and hedging it, no? As in, you make the same PnL on expiry. (But before expiry, PnL will be quite volatile obviously). That's my main point...
 
Quote from TskTsk:

Thanks for the input

Essentially my above point is that you hedge whatever premium you receive in a way that within expiry, gives you the exact same PnL you would expect from selling the premium at the 25D put instead. Because the 25D put has a more favorable theta/gamma ratio, hedging your premium against this ratio should be the same as actually selling the 25D put premium and hedging it, no? As in, you make the same PnL on expiry. (But before expiry, PnL will be quite volatile obviously). That's my main point...
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No. Otherwise I would sell straddles and hedge them at a vol of a million.
 
Quote from newwurldmn:

No. Otherwise I would sell straddles and hedge them at a vol of a million.
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That would be the same as not hedging the straddle at all, wouldn't it? Because you essentially expect to keep the entire straddle premium and thus see no need to hedge....
 
BTW I realize you aren't monetizing skew per se, as you say, it's quite complex and I probably should have used different terminology. My point is that by adjusting whatever gamma you hedge your premium at, you essentially re-price the IV that your premium was sold at. For instance if you hedge your premium at a lower gamma than the actual gamma of your position, you 'simulate' your premium having been sold at a higher IV than it actually has. Your risk goes to PnL volatility before expiry obviously.
 
Quote from TskTsk:

BTW I realize you aren't monetizing skew per se, as you say, it's quite complex and I probably should have used different terminology. My point is that by adjusting whatever gamma you hedge your premium at, you essentially re-price the IV that your premium was sold at. For instance if you hedge your premium at a lower gamma than the actual gamma of your position, you 'simulate' your premium having been sold at a higher IV than it actually has. Your risk goes to PnL volatility before expiry obviously.
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Yes. But all this does is introduce noise into your pnl. It doesn't change your expectation. Simulate it.
 
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