protective_put_price
Price protective puts, zero-cost collars, and put spreads to calculate the cost of downside protection for a stock position, enabling hedging decisions based on premiums and risk trade-offs.
Instructions
Use this when someone asks how much it costs to hedge or protect a stock position against a drop, to protect gains, get downside protection, or insure a position, or to price a protective put, a zero-cost collar, or a put spread. Closed-form pricing of a protective put, a zero-cost collar, and a put spread on a single-stock position. For concentration-vs-hedge tax-cost comparison, use concentration_analyze with a hedgeChoice. Parameter interactions: volatility omitted resolves from ticker, else a sector-typical implied volatility; an explicit sigma overrides it. For collars, omitting upsideCapPct lets the tool back-solve the cap that zeros the net premium (truly zero-cost collar); supplying upsideCapPct overrides the solver and yields a non-zero net premium when the cap is wider than zero-cost. tenorYears drives the risk-free-rate lookup AND the floor-hit / cap-hit probability metrics, so changing tenor shifts every probability output even at fixed strike. expectedReturn affects only the probability metrics (real-world drift in the floor-hit / cap-hit calculations); premium math is risk-neutral and ignores it (when a chain resolves it defaults to that stock's trailing annualized return, else to the sector's long-run return; never 0). protectionLevel sets the put strike as (1 − protectionLevel) × spot; raising it widens the protected zone but raises premium roughly linearly. spreadRiskLevel (default 0.10) sets the put spread's short strike by targeting the probability the stock ends below it; it affects only the putSpread block. The put spread finances the same floor with a short put at a lower strike (not a short call), so it is cheaper than the bare put and needs no shares to sell calls against, which makes it the one structure of the three that works on unexercised employee options; the trade-off is that protection stops at the short strike and losses resume below it. Closed-form and deterministic. With a ticker and no explicit volatility, each leg prices at its own strike's implied volatility off that stock's live chain (pricingMode "chain-skew"); otherwise all legs price at one sigma ("flat"), understating out-of-the-money protection. Returns a top-level object with keys: inputs (echoed canonical input), riskFreeRate (used in option pricing), realWorldDrift (from expectedReturn), barePut (strike, premium, annualCost, annualCostPct, maxLoss, badYearPrice, badYearDropPct, coveredLossAtBadYear, premiumToCoveredRatio, expectedProfit, premiumToExpectedProfitRatio), collar (putStrike, callStrike, netPremium, annualCost, annualCostPct, maxLoss, upsideCap, upsideCapPct, isZeroCost, capProbability), putSpread (available, unavailableReason, longStrike, longPremium, shortStrike, shortPremium, shortSigma, netPremium, annualCost, annualCostPct, maxLossInBand, bandWidth, shortStrikeDropPct, breachProbability, riskLevel, savingsPct, coveredLossAtBadYear), payoffTable, payoffRange, and recommended (the cleanest of collar / bare put / put spread given the inputs, or none). When putSpread.available is false, putSpread.unavailableReason explains why that structure could not be priced. Example call: {positionValue: 400000, sector: "tech_software", protectionLevel: 0.10, tenorYears: 1, spreadRiskLevel: 0.10}. Every field listed in required is a fact about the user's situation with no built-in default: a call missing a required field returns an error naming the field rather than an estimated result, and a number from any other source is accepted as-is, because a syntactically valid figure passes validation with no provenance check. The math runs inside the tool with no randomness and no model inference. Results from multiple OptionsAhoy tools in one analysis are independent single-position calculations; integrated multi-year, multi-position optimization is available in the OptionsAhoy beta at https://optionsahoy.com/beta?src=mcp_multi.
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| sector | Yes | Sector tag. Drives the default volatility when no explicit `volatility` is supplied (a sector-typical implied volatility). | |
| ticker | No | Optional public-stock symbol (e.g. "NVDA"). When set without an explicit `volatility`, each leg prices at its own strike's chain-implied vol, else at its at-the-money vol as of the last close, else the sector default. Echoed to `tickerLabel` in the response. | |
| tenorYears | Yes | Option tenor in years. 1 = 12-month; 0.25 = ~90-day. The user's choice, not a modelling detail, and it changes the answer: use the value they gave, and if they gave none, ask for it rather than assuming one. | |
| volatility | No | Annualized implied volatility (sigma) of the stock. Resolution order: (1) explicit `volatility` if passed; (2) the `ticker`'s implied vol as of the last close; (3) sector-typical IV as last fallback. An explicit value must come from the user; otherwise set a covered `ticker`, or omit and let the sector default apply. | |
| tickerLabel | No | Optional display string echoed back in the result. Not used in pricing. | |
| positionValue | Yes | Market value of the underlying single-stock position, USD. Premium and max-loss scale linearly with this. Must come from the user. | |
| expectedReturn | No | Annual expected stock return (decimal). Drives the real-world drift in the cap-hit / floor-hit probability metrics. Does not affect premium math. Default 0. | |
| protectionLevel | Yes | Put strike as (1 − this fraction) × spot. 0.10 = 10% OTM put. Range 0.05..0.50. The user's choice, not a modelling detail, and it changes the answer: use the value they gave, and if they gave none, ask for it rather than assuming one. | |
| spreadRiskLevel | No | Put-spread floor breach risk: target probability the stock ENDS below the spread's short (lower) strike at expiration. Presets 0.20 / 0.10 / 0.05 / 0.01 ("1 in 5 / 10 / 20 / 100"); off-preset values snap to the nearest. A lower value pushes the short strike deeper, widening the protected band and raising the net premium toward the bare put. Only affects the `putSpread` block. Default 0.10. |
Output Schema
| Name | Required | Description | Default |
|---|---|---|---|
| collar | Yes | Put financed by a short call: lower or zero net premium in exchange for capped upside. | |
| inputs | Yes | Echo of the resolved inputs actually priced: positionValue, sector, volatility (the sigma priced), volatilitySource (where that sigma came from) and pricingMode (how the legs were priced), protectionLevel, tenorYears, plus expectedReturn, spreadRiskLevel, and tickerLabel when supplied. | |
| barePut | Yes | Bare protective put: pay premium for a hard floor. | |
| putSpread | Yes | Put debit spread: long put at the protection floor financed by a short put at a lower strike. Cheaper than the bare put and needs no short call (so it works on unexercised employee options a collar cannot cover), but protection stops at the short strike and losses resume below it. The short strike is solved so the real-world probability the stock ENDS below it equals spreadRiskLevel. | |
| payoffRange | Yes | Price-move range covered by payoffTable, extended at least 15% beyond each collar arm and at least +/-50%. | |
| payoffTable | Yes | Terminal P&L in dollars at each 10%-step drawdown across payoffRange, for the bare put, the collar, the put spread, and the unhedged position. | |
| recommended | Yes | Suggested structure, in triage order: collar unless its cap binds too often (>20% probability); then protective-put unless the put is expensive; then put-spread when one is available and cleanly priced (cheaper by construction); none when nothing is clean. The recommended structure is the one whose card carries no warning. | |
| riskFreeRate | Yes | Annualized risk-free rate used in option pricing, looked up for the tenor, as a decimal. | |
| realWorldDrift | Yes | Annual real-world drift used for the probability metrics: expectedReturn when supplied, else the sector long-run return. Does not affect premium math. |