Maths Calculator

Advanced Cliquet Option Pricing Calculator

Analyze periodic returns, local caps, and global limits. See pricing, payoff, and credited path details. Export reports, compare inputs, and understand structure behavior quickly.

Cliquet option input form

Large screens use three columns, smaller screens use two, and mobile uses one.

Starting underlying level.
Annual continuously compounded rate approximation.
Annual dividend or carry yield.
Annualized volatility input.
Total term of the trade.
Monthly uses 12, quarterly uses 4.
Coupon leg notional amount.
Scales the sum of credited returns.
Added before global floor and cap.
Minimum credited return each reset.
Maximum credited return each reset.
Minimum total coupon rate.
Maximum total coupon rate.
Higher values improve stability but take longer.
Optional reproducibility control.
Example: $, €, £, Rs.

Formula used

This calculator prices the coupon option leg of a cliquet structure with Monte Carlo simulation under geometric Brownian motion.

Path evolution: S(t+Δt) = S(t) × exp((r - q - 0.5σ²)Δt + σ√Δt Z)

Periodic raw return: Rᵢ = Sᵢ / Sᵢ₋₁ - 1

Credited reset return: Cᵢ = min(Local Cap, max(Local Floor, Rᵢ))

Aggregate rate before global limits: A = Guaranteed Coupon + Participation × ΣCᵢ

Bounded rate: B = min(Global Cap, max(Global Floor, A))

Coupon option payoff: Payoff = Notional × max(B, 0)

Present value: Price = e^(-rT) × average simulated payoff

This setup is suitable for capped and floored reset coupons. It does not include separate bond principal repayment or issuer credit adjustments.

How to use this calculator

  1. Enter the starting spot, annual rate, dividend yield, and volatility.
  2. Set maturity and the number of reset periods for the contract.
  3. Enter notional, participation, guaranteed coupon, and local cap and floor terms.
  4. Enter the global cap and floor that apply to the total credited coupon.
  5. Choose the number of Monte Carlo paths. More paths usually improve stability.
  6. Optionally add a random seed so repeated runs produce the same simulation.
  7. Submit the form to see the price, confidence interval, tables, and the Plotly graph.
  8. Use the CSV and PDF buttons to export the summary and period breakdown.

Example data table

This sample configuration gives you a realistic monthly reset scenario for testing the calculator.

Input Example value Meaning
Initial spot price 100 Starting underlying level.
Risk-free rate 4% Annual discounting rate.
Dividend yield 1% Annual carry adjustment.
Volatility 22% Annualized return dispersion.
Maturity 1 year Total contract term.
Reset periods 12 Monthly reset structure.
Participation 100% Full exposure to credited returns.
Local floor / cap 0% / 3% Per-period credited return limits.
Global floor / cap 0% / 24% Total coupon bounds.
Guaranteed coupon 0% Base coupon added before global limits.
Notional 100,000 Coupon payoff base amount.
Paths 5,000 Simulation sample size.

Frequently asked questions

1) What is a cliquet option?

A cliquet option resets periodically. Each reset locks a capped and floored return, then the contract aggregates those credited returns into a final coupon or payoff.

2) Why use Monte Carlo here?

Monte Carlo handles path-dependent features naturally. It is useful when local caps, local floors, guaranteed coupons, and global limits interact in ways that make simple closed-form pricing less practical.

3) What does the local cap do?

The local cap limits each reset return. A very strong period cannot contribute more than the cap, which reduces upside but also makes the coupon path smoother.

4) What does the local floor do?

The local floor limits downside for each reset. If a raw period return falls below the floor, the credited return is raised to that floor for aggregation.

5) What is the difference between local and global limits?

Local limits apply to every reset separately. Global limits apply once, after all credited returns and any guaranteed coupon have been combined into one total rate.

6) Does this price include principal protection?

No. This calculator prices the coupon option leg only. A principal-protected note would also require a bond component and possibly issuer credit adjustments.

7) Why does the result change slightly between runs?

Monte Carlo uses random sampling. Small differences are normal. Increase the number of paths or enter a fixed random seed to make the run more stable and reproducible.

8) What does the confidence interval mean?

It gives a simulation uncertainty band around the estimated present value. Narrower intervals usually mean the run used enough paths and produced a more stable estimate.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.