Calculator Inputs
Example Data Table
These rows are illustrative examples for quick testing and discussion.
| Scenario | Style | Type | Spot | Strike | Vol % | Time | Illustrative Premium |
|---|---|---|---|---|---|---|---|
| Baseline hedge | Fixed | Call | 100 | 100 | 25 | 1.00 | 22.8400 |
| Downside study | Fixed | Put | 100 | 100 | 25 | 1.00 | 18.1300 |
| Trend capture | Floating | Call | 100 | N/A | 20 | 0.75 | 14.6200 |
| Reversal hedge | Floating | Put | 100 | N/A | 20 | 0.75 | 13.9100 |
| High-vol case | Fixed | Call | 100 | 95 | 40 | 1.50 | 38.2700 |
Formula Used
This calculator uses a risk-neutral Monte Carlo model with discrete monitoring. The underlying price is simulated with geometric Brownian motion:
S(t+Δt) = S(t) × exp((r - q - 0.5σ²)Δt + σ√Δt × Z)
Where r is the risk-free rate, q is the dividend yield,
σ is volatility, and Z is a standard normal shock.
Payoff Rules
- Fixed-strike call:
max(MaxPath − K, 0) - Fixed-strike put:
max(K − MinPath, 0) - Floating-strike call:
max(ST − MinPath, 0) - Floating-strike put:
max(MaxPath − ST, 0)
The final premium is the discounted average payoff:
Option Value = e^(−rT) × Average Payoff
Delta, gamma, vega, rho, and theta are estimated numerically by bumping one input at a time and repricing the option.
How to Use This Calculator
- Choose fixed-strike or floating-strike lookback style.
- Select call or put depending on your payoff direction.
- Enter spot, strike, rate, dividend yield, volatility, and time to maturity.
- Set monitoring steps and simulation paths for accuracy.
- Keep antithetic variates enabled for steadier Monte Carlo estimates.
- Press Price Option to see premium, Greeks, and the Plotly price curve.
Frequently Asked Questions
1. What is a lookback option?
A lookback option is an exotic derivative whose payoff depends on the best price reached during the option’s life. That path dependence lets the holder benefit from the maximum or minimum observed price, not only the expiry price.
2. What is the difference between fixed and floating lookbacks?
Fixed-strike lookbacks compare the path extreme with a preset strike. Floating-strike lookbacks set the effective strike from the path minimum for calls or the path maximum for puts.
3. Why do monitoring steps matter?
Monitoring steps control how often the path is observed. More steps capture highs and lows more accurately, but they also increase runtime. Too few steps can understate path-dependent value.
4. Why do simulation paths matter?
More paths reduce Monte Carlo noise and usually narrow the confidence interval. The tradeoff is speed. For practical use, increase paths until the premium becomes stable enough for your decision.
5. How does dividend yield affect pricing?
Higher dividend yield lowers expected growth under risk-neutral pricing. That often weakens call values and can support put values, depending on whether the contract benefits from path highs or path lows.
6. Are the Greeks exact?
No. The Greeks here are numerical sensitivity estimates from small parameter bumps. They are useful for risk analysis, but they can still be noisy when path counts are low.
7. Why is strike ignored for floating-strike options?
Floating-strike lookbacks use the path minimum or path maximum as the effective strike. Because of that payoff structure, the separate strike field does not affect the premium.
8. Will this match market quotes exactly?
It gives a model estimate, not a guaranteed market quote. Real quotes may also reflect volatility surfaces, monitoring conventions, funding assumptions, liquidity, and dealer margins.