Assuming positive skew premium & continuously delta hedged, is selling OTM strangle always a superior strategy than selling ATM straddles (hence P&L is theoretically simplified as 0.5 * Gamma * Spot ^2 * (IV^2 - RV^2)), since OTM IV is higher? Thanks.
2 Answers
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This is a bit like saying it's "a superior strategy" to lend $100 for 2 years rather than for 1y year because you earn twice as much interest. The skew premium is there to reflect directional risk in the underlying rebasing itself to a materially different level, and the market participants' anticipated impact on demand/supply of options written on that underlying such a rebasing would entail. Moreover, most markets have a directional bias which drives the skew: for example in EM FX options markets the bias is to a sell-off rather than a rally so OTM calls > OTM puts. It may well be that the skew premium may be being overpriced - in which case options traders "sell flys" i.e. buy atm straddles vs selling strangles. So I would remove the "always" from your statement and make it subjective.
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$\begingroup$ Hi @user35980, thanks a lot for the insightful reply. a follow up question would be: if the short volatility (either straddle or strangle) position is continuously hedged (theoretically), so the P&L would be 0.5 * gamma * spot ^2 * (implied volatility ^2 -realized volatility ^2). and under this setting, I would assume no directional bias involved (again theoretically). then in this case, is OTM strangle a better choice, given it has a higher implied volatility. Thanks a lot. $\endgroup$– wjdSep 23 at 12:45
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$\begingroup$ even if you had perfect continuous delta hedging, it doesn't address the liquidity (demand/supply) issue impact. consider this: s&p500 is trading around 4300 right now and has been in a range of +/-500 over the last year or so. so you have ample buyers and sellers of both, say 3m, calls and puts. if, following some calamitous event, it sold off to 2000 in the next 3 weeks - do you think people will be as confident writing puts (or even calls for that matter)? using that logic to write a 2000 strike put today, anyone would charge a significant rebasing premium - that's the skew premium. $\endgroup$ Sep 23 at 13:06
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There's a reason why the otm IVs are higher to begin with.
Market moves/returns exhibit kurtosis. This implies most of the time they move in a confined range, from time to time they exhibit very large moves. When they exhibit very large moves, you probably don't want to be short cheap tails. Hence rational traders would demand a premium to be short these, driving up the price and thus vols of otm options.
Each market has its own dynamic and thus Skew shape.
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$\begingroup$ Hi @user68819, thanks a lot for the detailed explanation about the volatility dynamics. Really appreciate. So, my follow up question here (as I also posted under user35980's reply): if the short volatility (either straddle or strangle) position is continuously hedged (theoretically), so the P&L would be 0.5 * gamma * spot ^2 * (implied volatility ^2 -realized volatility ^2). Under this setting, I would assume 0 delta and hence large directional moves will not cause significant P&L. Then in this case, is OTM strangle a better choice, given it has a higher implied volatility. Thanks a lot $\endgroup$– wjdSep 23 at 12:48
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$\begingroup$ Sorry, no. Those theorems about continuous hedging require a lognormal distribution and iid returns. The actual returns differ fom this (kurtosis, etc.), hence the skew. $\endgroup$– nbbo2Sep 23 at 13:09
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$\begingroup$ @wjd..markets don't work like text books. When the market gaps, it gaps. You won't have time to do anything. So you can forget about theoretical constructs..which is why a smile exists. There is no continuous hedging and/or continuous processes. Market is jumpy and abrupt and fat tailed..all reasons for a Skew or smile to exist. Think the confusion here may be you are mixing a theoretical construct/ approx with a very practical concept. Try it on a spreadsheet. $\endgroup$ Sep 23 at 21:21
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$\begingroup$ Thanks @ nbbo2 and @user68819, for the kind sharing. your insights are invaluable. $\endgroup$– wjdSep 24 at 4:37