Hedging Digital Calls Near Expiration with Call Spreads
Summary
The question highlights why dynamic delta hedging a digital option can become difficult near maturity: around the strike, small underlying price moves can cause large changes in the option’s value and delta. It asks whether a static call spread is preferable near expiration and when to switch to that hedge.
The response cautions that a tight call spread near maturity may be hard to source because a counterparty would inherit substantial gamma and pin risk. A potential counterparty may already want to reduce similar exposure, but the note offers no proof that static hedging is generally more beneficial and gives no quantitative comparison of costs or risks. It suggests discussing an early closeout with the original dealer as a practical possibility. The guidance is qualitative and market-dependent; it does not specify a hedge ratio, spread width, or switching rule.
Key ideas
- A digital option’s delta can change sharply near the strike as expiry approaches.
- A tight call spread can transfer some exposure, but counterparties may be reluctant to accept its gamma risk.
- Pin risk near the strike can make late-stage hedging difficult.
- The note gives no general proof or timing rule for switching from dynamic to static hedging.
Tags
Full text
# Hedging digital calls # Hedging digital calls From what I have read, digital options are difficult to hedge near expiration because, around the strike, small moves in the underlying asset price can have very large effects on the value of option and the option delta. This means we would have to buy/sell large amounts of shares frequently to stay well hedged when using dynamic delta hedging. It seems that near expiration of the option it is better to use a static call-spread hedge. - When is the best time to switch from dynamic hedging to a call-spread hedge? For example one example question I am reading asks "would you build your call spread hedge the day prior to maturity"? - Is there anyway to prove that it is more beneficial to use static hedging near expiry? ## Answer by FinanceGuyThatCantCode (score 3) https://quant.stackexchange.com/a/33318 You theoretically could just trade the call spread at the beginning and more or less forget about it - theoretically. In reality, what counterparty would be willing to trade a very tight call spread with you close to expiration? Why would they want to take on the gamma risk you are trying to unload? Maybe they are already loaded with gamma, so you maybe can come to them with the trade that will help them unload some gamma - but you might as well just try to trade out of your digital call and call it a day. The pin risk around the money near expiration is something nobody wants. Best bet is to call the bank you traded with and ask if they would like to take off the trade - they would probably love to get rid of that kind of toxic waste.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.