Quantifying Hedging Error Due To Expiration Day Range?

Question

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?

Answer 1

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.

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