protective_put_price

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. Use for standalone hedge pricing on a single-stock position; for concentration-vs-hedge tax-cost comparison, use concentration_analyze with a hedgeChoice. Parameter interactions: volatility omitted falls back to 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 (default 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, deterministic, offline: sector volatility table and risk-free-rate curve compiled in. Reports annualized hedge cost as a percentage of position value, maximum loss with the hedge in place, upside-participation cap (collar only, since the short call offsets the long put premium), and probability of hitting the protection floor over the tenor. 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). The barePut, collar, and putSpread blocks are always returned regardless of caller preference. 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 optionsahoy.com/beta?src=mcp_multi.