Delta for option sellers: what 25-delta means
Delta in plain terms for people who sell options: what it measures, why traders read it as a rough probability, and what a 25-delta put did in our replays.
What delta is
Delta is how much an option's price moves when the underlying moves one dollar. A put with a delta of minus 0.25 gains about a quarter of a point in value for every one-point drop in the stock. Sellers usually drop the sign and call it a 25-delta put.
Delta changes as the stock moves and as time passes. A put that starts at 25 delta can become a 50-delta put if the stock falls to the strike, and drift toward zero if the stock rises and expiry approaches.
Delta as a rough probability
Traders use delta as a shorthand for the chance the option finishes in the money. A 25-delta put is read as roughly a one-in-four chance of expiring below the strike. The approximation comes from the pricing model, not from history, so treat it as the market's estimate, not a promise.
In our replays of 25-delta puts held 30 to 45 days, the share of trades that finished in the money and were assigned ran about 20% to 37% depending on the ticker, which sits around the one-in-four the delta implied.
What 25 delta earned
Selling a 25-delta put on QQQ 30 to 45 days out and holding to expiry earned about +0.5% a trade on the cash set aside across 2016 to 2026, with a 94% win rate and a worst single trade of minus 21.5% of collateral. The win rate looks better than the one-in-four delta suggests because many assigned trades still keep enough premium to finish positive.
The same short strike as part of a put credit spread with a 5% wing earned about +6.0% a trade on dollars at risk. Delta sets where the strike sits; the structure decides how much capital the trade ties up.
Choosing a delta
Lower delta means a strike further out of the money: a higher win rate, smaller premium, and losses that come less often but are not smaller when they come. Higher delta means more premium and more assignments. There is no free lunch along this line; delta trades frequency of losses for size of credit.
Delta also hides correlation. Five 25-delta puts on tickers that move together behave like one large position. In our paper book the scanned tickers had a mean pairwise correlation of 0.46, which works out to about two independent bets a week. The guide on picking a strike covers how delta fits with the other choices.
Historical replays are not a forecast. Options can lose more than the premium collected. This is education, not a recommendation to trade anything.