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In a live example: Today is June 14, 1 hour before market close, and \$SPY (S&P 500 ETF) is currently at \$372.28 and the June 15 \$350 strike Put is being quoted for \$0.13 on the bid and \$0.14 cents on the ask. The IV is 39.00%.

The $350 strike is currently 5.98% away from the spot/ATM price.

An implied volatility of 39% means that $SPY must realize a minimum of 2.45% volatility for the MM to break-even, and more than that for the MM to profit. 0.39*sqrt(1/252)*100 = 2.4567...

Let's say many traders come into the market and sell these puts to the MM at the bid, 5000 contracts for example. So now the MM has paid \$65,000 and is long 5000 of the June 15 $350 Puts, he delta-hedges respectively.

More and more traders keep coming in and selling this put and other puts around this strike. The MM over the course of the trading day continues to purchase a lot of winger options in his inventory and is long skew and convexity.

The bid-ask spread on this individual $350 strike put is only 1 cent. As are the majority of the bid-ask spreads on all deep OTM options (both calls and puts) on these short-dated SPY tenors.

We know that vol skew exists, and these deep OTM Options' implied vols are greatly overpriced most of the time. Buying them (while delta-hedging or not) will lead to losses as they expire worthless and never realize the volatility needed for a buyer who delta-hedges to even breakeven.

Say tomorrow $SPY realizes only 1% volatility, the MM will lose on his massive long skew/tails position of various different deep OTM put strikes on these weekly tenors.

My question is, how do MMs profit at all when they have to provide liquidity and purchase these short-dated deep OTM winger options that are quoted at high implied vols (skew) and majority of the time never end up realizing the vol needed for the MM to profit? With a 1 cent bid ask spread on these deep OTM options, how is there any room for the MM to buy below theo and profit off the spread?

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In the situation that you describe, the MM will indeed probably lose a large part of the premium, but also has a small chance of making a large amount of money if the market completely falls apart. Thus, the book is not balanced and the MM has to live with that profile. If you think it’s a bad situation, would you prefer to be the other way round ? Short 5000 wing strikes for 65k? It doesn’t make for a good night’s sleep.

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  • $\begingroup$ For the past couple years, there have been consistent sellers (hedge funds, institutions, retails) looking for carry who harvest skew in short dated tenors, how are MMs dealing with this profile? It's historically unprofitable and negative expected value to buy tails. $\endgroup$
    – user46424
    Jun 14, 2022 at 20:24
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I think the answer to this question is that it's not as simple as you're making it out to be.

If I'm market making options, there is no requirement that I hedge that option with the exact same strike. Perhaps I am happy to sell a different (portfolio of) option(s) such that I am net receiving premium and am comfortable with the risk I have left?

If I have bought X OTM options, I can sell some smaller number of ATM options such that I'm net receiving premium and still long gamma in a large market move.

Alternatively, maybe it allows me to leave the book with a long bias and not have to worry about a sharp move down hurting me.

Alternatively, there are many market makers out there - perhaps one of them is short some of the strikes that are being sold in the market - if I were short \$190m of puts and could buy back the var for $65k I'd strongly consider it.

I'm curious how you are confident saying that these options are greatly overpriced on a 39% vol given that the last three days SPX has moved between 2.4% and 3.9% each day. In a market where we've just had three consecutive down days totaling just shy of a 9% drop, I'm not so sure I would be so comfortable selling those options...

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  • $\begingroup$ Indeed has the SPX has been making large realized volatility moves lately, but I only used it as for example purposes. If you had bought the put and delta-hedged yesterday, you would've lost money today. It's proven that buying tails is -negative expected value and loses money over the longterm. Buying back some short var makes sense to change your book's profile. Selling ATM/buying OTM makes sense too. But my question is how MMs have been dealing with SPY tail sellers looking for carry in front month tenors since they options have a 1 cent spread (no profit for MM) and lose money 50%> of time $\endgroup$
    – user46424
    Jun 16, 2022 at 4:07
  • $\begingroup$ i don't think you can make the statement that buying tails is negative expected value. $\endgroup$
    – will
    Jun 16, 2022 at 22:00
  • $\begingroup$ Buying tails, deep OTM puts, is negative expected value. You can look at the empirical results yourself on whatever timeframe you'd like based on X% moneyness away from the S&P500's starting price and compare it to the timeframe's closing price. They expire worthless the majority of the time and skew is overpriced in indices. $\endgroup$
    – user46424
    Jun 17, 2022 at 2:40
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    $\begingroup$ It depends where your value comes from. If you work somewhere that requires reserving cash to cover a percentage of your VaR then in some cases it makes sense to hold the tails as it's cheaper than reserving cash. Likewise, in many environments it's not a wise move career wise to sell the wings for the carry as your personal utility function places a much higher cost on those events where you lose a large amount of money on a tail event vs harvesting a small carry. There is additional value to this, which is why it looks systematically overpriced vs a theory that neglects these benefits. $\endgroup$
    – will
    Jun 19, 2022 at 1:05
  • $\begingroup$ Additionally, the cost of selling those puts is actually higher than the premium, as you'll have to post substantial margin, which you'll have to fund at a non zero rate. $\endgroup$
    – will
    Jun 19, 2022 at 1:08

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