Expiration Mismatch and Static Hedging with Options
Summary
The document examines a static hedge for two short calls with the same strike but different expirations, using one call whose expiration falls between theirs. The example shows that matching total notional does not keep the hedge balanced over time: the shorter liability expires first, leaving the asset call larger than the remaining liability, and the asset later expires before the longer liability. The response describes the resulting position as a time spread and notes that a hedge sized to cover both liabilities requires two middle-expiration calls.
The practical lesson is that this static hedge only offsets the liabilities up to the first expiration; the position must then be rehedged or unwound to avoid changing exposure. The discussion does not quantify price sensitivity, volatility effects, or the value of the residual positions. It also does not establish a general rule for selecting an asset strike, so a notional-weighted strike is not evaluated.
Key ideas
- Equal strikes and total notional do not ensure a balanced hedge across different expirations.
- A middle-expiration call sized to cover both liabilities creates a time-spread position.
- After the first liability expires, the hedge has more near-term call exposure than remaining liability.
- Once the hedge expires, any longer-dated liability is left uncovered unless the position is adjusted.
- The response recommends rehedging or unwinding as expirations pass.
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Full text
# Quantifying Hedging Error Due To Expiration Day Range? # Quantifying Hedging Error Due To Expiration Day Range? 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 - Are the numbers in my post correct (or basically, am I understanding this problem correctly) - 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? - 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 by user508 (score 2) https://quant.stackexchange.com/a/1366 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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