{
  "id": "9bdcb0a9-27d3-509c-bc22-d24db878c22a",
  "slug": "cap",
  "term": "Cap",
  "aliases": [],
  "category": "Derivatives & Options",
  "category_slug": "derivatives-options",
  "difficulty": "intermediate",
  "definition": "An interest rate cap is an over-the-counter derivative contract that pays the buyer the difference between a floating reference rate and a specified strike rate whenever the reference rate exceeds the strike, providing protection against rising interest rates on a notional principal amount.",
  "key_takeaways": [
    "A cap is a series of caplets — individual call options on the reference rate (e.g., SOFR, EURIBOR) — each covering one reset period.",
    "The cap buyer pays an upfront premium and receives payments when the reference rate exceeds the cap rate, effectively capping their floating-rate borrowing cost.",
    "Cap premium is driven by implied volatility, the distance between current rates and the cap strike, time to expiration, and the forward rate curve.",
    "Caps are used by floating-rate borrowers (corporations, real estate operators) to hedge against rising rate environments.",
    "The Black (1976) model is the market standard for pricing individual caplets using a log-normal distribution for forward rates."
  ],
  "detailed_explanation": "An interest rate cap is structured as a portfolio of caplets, each of which is a call option on a specific reference rate (e.g., three-month SOFR) for a future period. If the cap rate is 4.0% and a $100 million notional cap has quarterly resets, then at each reset date, if three-month SOFR exceeds 4.0%, the cap seller pays the buyer: Notional × max(Reference Rate − Cap Rate, 0) × (Days/360). This payment compensates the borrower for the excess interest they owe on their floating-rate loan.\n\nThe Black (1976) model prices each caplet as: Caplet = N × τ × P(0, T) × [F × N(d1) − K × N(d2)], where N is notional, τ is the accrual period, P(0,T) is the discount factor, F is the forward rate, K is the cap strike, and d1 and d2 follow the standard log-normal formula with σ as the caplet's implied volatility. Market participants quote caps in terms of flat volatility (a single vol applied to all caplets) or forward volatility (caplet-by-caplet implied vol), with the latter providing richer information about the vol term structure.\n\nThe premium economics of a cap reflect the trade-off between insurance cost and protection level. Deep out-of-the-money caps (strike well above current rates) are cheap but provide protection only against large rate increases. At-the-money caps are more expensive but activate quickly if rates rise moderately. The concept of the breakeven rate is critical: if a borrower pays 80 bps for a cap, the total hedged borrowing cost equals the cap rate plus 80 bps; this must be weighed against the unhedged floating rate plus spread.\n\nCaps are frequently combined with floors (interest rate puts) to create collars, where the borrower sells a floor to partially offset the cost of the cap. When the floor strike equals the cap strike, the resulting instrument is an interest rate swap. This relationship — cap minus floor equals a swap — is a fundamental no-arbitrage identity in the rates market.\n\nFrom a risk management perspective, cap books at broker-dealers require active delta hedging against changes in forward rates and vega hedging against changes in implied volatility. The sensitivity of a cap's value to a parallel shift in the yield curve (the cap's delta) requires offsetting positions in swaps or futures. As rates approach the cap strike, gamma (the rate of change of delta) increases significantly, requiring more frequent rebalancing.",
  "example": "A real estate company has a $200 million floating-rate construction loan tied to three-month SOFR plus 175 bps, with two years remaining. Concerned that SOFR could rise from the current 5.2% to 7%+, the CFO purchases a two-year cap with a 6.0% SOFR strike for a premium of 60 bps ($1.2 million). If SOFR rises to 7.5% at the next reset, the cap pays $200M × (7.5% − 6.0%) × (90/360) = $750,000, offsetting the incremental interest cost. The total effective borrowing rate is capped at 6.0% + 1.75% + 0.60% (premium amortized) = approximately 8.35% all-in, regardless of how high SOFR rises.",
  "formula": "Caplet Payoff = Notional × max(Reference Rate − Cap Rate, 0) × (Days/360)",
  "formula_latex": null,
  "interactive_type": "calculator",
  "calculator_id": null,
  "related_terms": [
    "arbitrage",
    "at-the-money",
    "call-option",
    "caplet",
    "convergence",
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    "delta",
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    "gamma",
    "hedging",
    "implied-volatility",
    "interest-rate",
    "interest-rate-cap",
    "interest-rate-swap",
    "naked-option"
  ],
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  ],
  "cross_references": [
    "arbitrage",
    "at-the-money",
    "call-option",
    "caplet",
    "delta",
    "floor",
    "gamma",
    "hedging",
    "implied-volatility",
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    "option",
    "out-of-the-money",
    "premium",
    "swap",
    "vega",
    "volatility",
    "yield",
    "yield-curve"
  ],
  "tags": [
    "level:intermediate",
    "cat:derivatives-options"
  ],
  "asset_classes": [
    "derivatives"
  ],
  "regulators": [],
  "see_also": [],
  "sources": [],
  "wordcount": 679,
  "checksum": "8049b9e8f3e99aa0",
  "version": "2026.05.03",
  "license": "CC-BY-4.0",
  "updated_at": "2026-09-07T02:15:24+00:00",
  "_links": {
    "self": "https://hedgefund.wiki/api/v1/terms/cap",
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    "markdown": "https://hedgefund.wiki/api/v1/terms/cap?format=md",
    "graph": "https://hedgefund.wiki/api/v1/graph/cap",
    "category": "https://hedgefund.wiki/api/v1/categories/derivatives-options",
    "schema": "https://hedgefund.wiki/schema/term.schema.json",
    "html": "https://hedgefund.wiki/#/terms/cap"
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}