Managing Inventory and Tail Risk in Deep Out-of-the-Money Options
Summary
The document asks how market makers handle heavy customer selling in short-dated, deep out-of-the-money options. Its example describes a dealer buying puts, delta-hedging, and accumulating long exposure to volatility skew and tail convexity. The question focuses on the apparent mismatch between high implied volatility, frequent expirations without value, and narrow quoted spreads.
The answers explain that a dealer can accept a position with many small premium losses and a low-probability large payoff, though that leaves the book exposed to adverse risk. Dealers may also manage inventory across strikes or other options, shape the book’s net premium and gamma, or use customer flow to offset an existing short position. One answer challenges the assumption that the options are overpriced, pointing to recent large market moves as relevant context. The exchange gives qualitative risk-management possibilities rather than a complete model of market-maker profitability; it does not establish that the quoted options are mispriced or quantify hedging and portfolio costs.
Key ideas
- Delta hedging does not eliminate the volatility and tail exposure of long out-of-the-money options.
- A dealer who buys options may lose much of the premium while retaining exposure to rare, large moves.
- Inventory can be managed across strikes or option portfolios rather than by hedging each contract in isolation.
- Customer flow may offset an existing position elsewhere in a dealer’s book.
- Whether implied volatility is excessive depends on market conditions and cannot be inferred from the example alone.
Tags
Full text
# How do market-makers profit & manage inventory when customers sell a lot of deep OTM options? # How do market-makers profit & manage inventory when customers sell a lot of deep OTM options? 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? ## Answer by dm63 (score 2) https://quant.stackexchange.com/a/71242 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. ## Answer by will (score 0) https://quant.stackexchange.com/a/71247 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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