Selling options

Level 6 — strategy families. The only family here that is not a bet on direction.

The claim

People pay more for protection than it turns out to be worth, so selling it is profitable on average.

An option is a contract, and someone buying a put is buying insurance against a fall. Like all insurance it is usually priced above its expected cost, because the buyer is paying for certainty and the seller is being paid to carry uncertainty. Selling it collects that premium.

Arvo's rule is a put credit spread: sell a put near a chosen probability of finishing in the money, and simultaneously buy a cheaper one a fixed distance below. You collect the difference in premium as a credit. The bought put is what turns an open-ended risk into a known one.

You collect	the credit, up front
Your best case	keep all of it — the market stays above your short strike
Your worst case	the width between the strikes, minus the credit
You want	the market to go up, sideways, or down slowly

Three of four outcomes pay you. That is the attraction, and it is also the trap.

Why anyone believes it

The variance risk premium is real and measured. Implied volatility — what options are priced at — has historically exceeded the volatility that subsequently occurred, persistently, across decades. Sellers were paid for that gap. This is one of the better-documented premia in markets.

The buyers are not stupid, they are hedging. A fund with a mandate to limit losses buys puts whether or not they are good value. That is a structural, price-insensitive bid, and it is what you are selling into. You are being paid to absorb someone else's constraint.

Time is on your side. An option loses value as expiry approaches, all else equal. A seller's position improves by doing nothing, which is the only family here of which that is true.

Say the cost

The premium is compensation for a real risk, not a market inefficiency. You are being paid because the bad outcome is genuinely bad. Every so often it happens, and it arrives as one large loss across every position at once — because the thing that causes it is the thing that correlates everything. The long-run average is positive and the path includes days that end accounts.

What it looks like

A payoff that is flat and positive over most of the range, then falls off a cliff:

flowchart LR
    A["Market above<br/>short strike"] --> AA["Keep the full credit"]
    B["Between the<br/>strikes"] --> BB["Partial loss"]
    C["Below the<br/>long strike"] --> CC["Maximum loss:<br/>width − credit"]

    style AA fill:#1a7f37,stroke:#1a7f37,color:#fff
    style CC fill:#b62324,stroke:#b62324,color:#fff

put_spread takes these, and the shipped ruleset searches only the first two:

Parameter	Means
short_delta	roughly the probability the short put finishes in the money. 0.20 means about a one-in-five chance
dte	days to expiry when the spread is opened
width	the strike distance in dollars, which sets the maximum loss
take_profit	the fraction of the credit at which to close early
exit_dte	close with this many days left, regardless
rate, dividend_yield	stated, not implied — inputs to pricing rather than things to search

Note take_profit and exit_dte: a seller's two exits are "most of the money has been made" and "the remaining time is not worth the remaining risk". Holding a credit spread to expiry for the last few cents is the worst risk-reward in the trade.

When it fails

A fast fall through both strikes. Your loss maxes out and there is nothing to manage. This is the designed worst case and it is fine — if you sized for it.

Correlation arrives with the loss. Ten spreads on ten underlyings lose together, because a market-wide fall is what causes any of them to lose. The correlation_cap in Arvo's risk model exists for exactly this, and it refuses when the correlation is unknown rather than assuming it away.

The win rate seduces you into sizing up. Eighty percent of trades paying in full is a powerful sequence of small confirmations. It is also the shape that makes traders raise size right before the loss that needed them not to. Go back to the expectancy table: a 4:1 loss-to-win ratio at an 80% win rate is break-even before costs.

Volatility expansion hurts before price does. A spread can be deep underwater on a mark while price is still above your short strike, because what you are short got more expensive. If your sizing cannot tolerate that, you will close at the worst moment.

Test it

This family has a hard limit that no amount of patience removes:

Option history cannot be backfilled

No vendor serves an option quote after the fact. A chain that was not recorded on the day is gone forever. What Arvo has recorded is the entire universe of what the option rules can ever be studied on — the list is option-quotes/underlyings.json in the project, chosen for liquidity and said out loud, never for what the underlyings returned. The engine records each one's chain every fifteen minutes of the regular session. Which means: you cannot run a ten-year study here. You can study what you have recorded, starting from when you started recording.

Once you have chains, rulesets/credit.json:

{
  "name": "credit",
  "label": "SPY put spreads",
  "premise": "Selling a put a month out near a fifth delta keeps enough credit to pay for the falls.",
  "interval": { "step": 1, "unit": "day" },
  "kind": {
    "kind": "grid",
    "rule": "put_spread",
    "fixed": {
      "trade_size": 100.0,
      "width": 5.0,
      "take_profit": 0.5,
      "exit_dte": 21.0,
      "rate": 0.04,
      "dividend_yield": 0.013
    },
    "axes": { "short_delta": [0.15, 0.20, 0.30], "dte": [30.0, 45.0] }
  }
}

Six configurations. Everything but delta and expiry is pinned, deliberately: every axis is a trial that deflation counts, and this family has the least history to spend on a wide search.

What to read:

1. How much history you actually have. Before the verdict, before anything — a few months of recorded chains cannot answer a question about a strategy whose risk shows up once every few years. Expect Inconclusive and understand that it is correct.
2. The worst single trade. The average tells you nothing about this payoff shape. Find the largest loss on the Trades tab and multiply it by the positions you would have held simultaneously.
3. Whether the window contained a fall. If your recorded history has no sharp drawdown in it, you have measured the good half of the distribution only. Say so out loud when you interpret the result.
4. The sizing. The gate sizes this by the cash the worst case needs. A standard option contract is a lot of a hundred units of the deliverable, and a proposal for two and a half contracts is refused as NotWholeLot rather than rounded.

Watch

• (to be chosen) — how a credit spread's payoff is built from two options.
• (to be chosen) — the variance risk premium, and what sellers are paid for.

Next

Why a backtest lies — level 7, and the one that changes how you read everything above.