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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.

  1. 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"?
  2. Is there anyway to prove that it is more beneficial to use static hedging near expiry?
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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.

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  • $\begingroup$ Just to clarify I have sold a digital call option, in this example. When you say I might as well just trade out of the digital call, do you mean just keep delta hedging as best I can. $$$$ A counterparty might not want to trade a very tight call spread which perfectly hedges my short digital call position. However I would of thought I could go to the market and create a sythentic call spread with puts/calls.$$$$ $\endgroup$ – Calypso Mar 28 '17 at 21:45
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    $\begingroup$ By trade out of, I mean buy back the digital call and close the position. If you are trading listed products, probably hard to trade the call spread that is tight enough unless it is SPX or something. If it is FX, you need a counterparty and a call spread that is reasonably tight - they will know what you are trying to achieve even if you do not tell them. It is a tough situation to be in if you cannot close the position. Nobody wants taht because it is an unhedgeable coin flip. $\endgroup$ – FinanceGuyThatCantCode Mar 28 '17 at 21:54

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