Synthesizing barrier options for short expiration

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phattails

Can anybody explain or give a reference for synthesizing a barrier options contract that expires before the earliest contract date?
 
Thanks for the response. Unless I am mistaken, it looks like I would need shorter expirations, which won't work for this scenario.
 
Quote from phattails:

Thanks for the response. Unless I am mistaken, it looks like I would need shorter expirations, which won't work for this scenario.
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If you are trying to make markets in digital options, all you really need to do is to replicate the delta/gamma profile. So, even if you have a meaningful mismatch in terms of expiry, you simply trade a risk reversal to offset the gamma/theta and dynamically manage the delta. The real art is to get a good sense how wide you need to make your call/put spread to be comfortable managing that delta. Is that the answer you are looking for?
 
Quote from sle:

If you are trying to make markets in digital options, all you really need to do is to replicate the delta/gamma profile. So, even if you have a meaningful mismatch in terms of expiry, you simply trade a risk reversal to offset the gamma/theta and dynamically manage the delta. The real art is to get a good sense how wide you need to make your call/put spread to be comfortable managing that delta. Is that the answer you are looking for?
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I spoke too soon. You mentioned binary options, but I'm looking for replication for Barrier options. For example, if the earliest barrier option is 1 month out and I want to replicate one for 1 week out.

Thanks.
 
Quote from phattails:

I spoke too soon. You mentioned binary options, but I'm looking for replication for Barrier options. For example, if the earliest barrier option is 1 month out and I want to replicate one for 1 week out.

Thanks.
More...
I assume you only care about down-n-out puts and up-n-out calls, as they are a nasty ones. You barrier could be "decomposed" into a vanilla option and a digital, which in turn can be thought of as a broken fly. So, you are short gamma at the strike and short a risk reversal around the barrier level.

As an exotics book runner, your main risk is the continuous digital risk which you need to manage when the underlying gets close to the barrier. The disaster scenario is that the asset will NOT go through the barrier and you will end up decaying into the intrinsic. Second disaster scenario is that you end up trading the asset in process of hedging your long gamma and then the asset gaps through the barrier, so you lose money on your wrong-way position.

The shorter is the barrier/digital, the more "unpleasant" is the discontinuity and harder it is to manage. General recipe is to put a large barrier buffer and manage them in a separate book.
 
Ok yes, this makes perfect sense. I can tell you have experience doing this at a very high level, so thank you for dispensing your advice.
 
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