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So to get exposure to Variance risk premia one could use variance swaps, is there a equivalent security for jumps. Hedging against jump but not diffusion risk could allow one to take targeted exposure which could be good for leveraged investor for example. Now I know we could buy Out of the money puts, but that for a fixed known jump size. With unknown jump size, we need to buy a lot of OTM puts which is not really practical? so?

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The closest contract to this is gap risk which does trade, either as OTC swap (client looking for a hedge) or embedded inside a structured note (bank looking to recycle risk).

Basic starting point is daily close-to- close observations against a 80-90% putspread, cancel upon payment, equity payer receives a spread for being short the risk (major equity indices this is normally circa 30-40bps p.a., but is quite volatile price)

In the above setting, if asset moves -9.99% in a day, you are fine. If it moves -15%, you will pay 5% etc. Idea of putspread is to allow leverage of up to 10x.

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  • $\begingroup$ Spencer-Laven: Good point, I remember eg UBS having a CPPI note out which had an embedded gap risk element. Just for personal curiosity - do you have a termsheet at hand with such embedded gap-risk clauses ? $\endgroup$ – ZRH Mar 20 at 7:55
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    $\begingroup$ Some mathematical analysis of gap options here lpsm.paris/pageperso/tankov/gap_risk.pdf $\endgroup$ – Alex C Mar 20 at 12:39
  • $\begingroup$ @ZRH apologies, not one that is freely available $\endgroup$ – James Spencer-Lavan Mar 20 at 19:25
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    $\begingroup$ @AlexC I saw that paper back when it was published. Peter Carr mentioned it in a presentation I attended. I haven't read it for a long time but I recall a lot of the gap replication centred around weekly options, which weren't liquidity available at the time, but now are on many assets (eq & non-eq) $\endgroup$ – James Spencer-Lavan Mar 20 at 19:28

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