Enter Values
Black's Model Formulas
Pricing Results
Cap-Floor Parity
Per-Period Breakdown
| Period | tk (yrs) | tk+1 (yrs) | Fk | d1 | d2 | P(0,tk+1) | Price ($) |
|---|
Formula Breakdown (First Caplet)
Model Assumptions
- Black's model applied independently to each caplet/floorlet
- Lognormal forward rate distribution (standard pre-2008 convention)
- Flat forward rate term structure (all forward rates equal F)
- Flat volatility surface (single σ applies to all periods)
- Day count simplified as 1/frequency (e.g., 0.25 for quarterly)
- Continuous discounting: P(0,t) = e−rt
- First period excluded (rate already known at inception)
For educational purposes. Not financial advice. Market conventions simplified.
Understanding Interest Rate Caps & Floors
What Are Interest Rate Caps and Floors?
An interest rate cap is a derivative that protects the holder against rising interest rates. It consists of a series of call options on a floating interest rate, called caplets. Each caplet pays the holder when the reference rate exceeds the cap rate (strike) for that period.
An interest rate floor is the opposite — it protects against falling rates. It consists of floorlets, which are put options on the floating rate. A collar combines a long cap with a short floor, often structured to be zero-cost.
Where d1 = [ln(F/RK) + σ²t/2] / (σ√t) and d2 = d1 − σ√t
Cap-Floor Parity
Cap-floor parity is analogous to put-call parity for equity options:
= L × Σ δk × P(0, tk+1) × (Fk − RK)
A long cap combined with a short floor produces the same cash flows as a pay-fixed interest rate swap at rate RK. This relationship can be used to verify pricing consistency and to construct synthetic instruments.
Practical Applications
- Borrowers buy caps to limit maximum borrowing cost on floating-rate debt while retaining the benefit of lower rates
- Investors buy floors to guarantee a minimum return on floating-rate investments
- Collars (cap + short floor) provide cost-effective hedging by financing the cap premium with floor income
Frequently Asked Questions
Disclaimer
This calculator is for educational purposes only. It uses Black's lognormal model with a flat forward rate assumption, which simplifies the actual term structure. Real-world cap/floor pricing uses individual forward rates from the yield curve and may employ different volatility models. This tool should not be used for trading decisions.
