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Let's say I have two call option liabilities that I want to statically hedge with a single call option.

Liabilities:

Liab_Call_1: Strike: 100 Notional: 1000 DaysToExpiration: 20

Liab_Call_2: Strike: 100 Notional: 1000 DaysToExpiration: 30

Assets:

Asset_Call_1: Strike: 100 Notional: 2000 DaysToExpiration: 25

In this case, I can see that after 25 days when my Asset_Call_1 expires, my Liab_Call_2's 1000 notional will be unhedged for 5 days.

Questions

  1. Are the numbers in my post correct (or basically, am I understanding this problem correctly)

  2. Is this as far as I can go in my quantification of the exposure after my assets expire? Are there any further metrics I can use to tell the effect of a trade day range on my hedge?

  3. Is taking the weighted average strike (by notional) of the liabilities the best way to calculate the strike of the asset?

Addendum

I was thinking about this a bit more, and actually, after 20 days, there are 5 days where the Asset_Call_1's notional exceeds my liability notional by 1000. So from day 20-25, there is 1000 extra notional that is hedged, and from 25-30 there is 1000 notional that is unhedged. So in this case, you could describe your hedging error as:

  • 5 days of 1000 overhedged (is this the right word) notional
  • 5 days of 1000 unhedged notional

Does that sound right at all?

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Your assumptions are that there are 3 call options, all struck at 100, all with contract multipliers of 10 and with maturities, 20 days, 25 days, and 30 days. You are short 1 of the 20 day calls and short 1 of the 30 day calls. You want to hedge with the 25 day call.

So, you'll buy 2 of those (1 to hedge the 20 day call, and 1 to hedge the 30 day call), and now you're short a time-fly. If you don't unwind it, then when the front leg expires, you'll be left with an unbalanced time spread (i.e. long 2 near-term, short 1 longer term). When the middle expires, you're left naked short a call. So, the static hedge is only good until the first option expires. Then you have to rehedge, or unwind.

Now, please see What kind of questions can I ask here

Specifically, the 1st paragraph: The Quantitative Finance Stack Exchange is intended for professionals and academics involved in securities valuations, risk modeling, and other topics related to quant modeling or trading. Basically, if you aren't earning a living at this, it's probably off topic

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