Estimated Price
Simulating...
Statistical estimate unavailable
Discounted Monte Carlo mean
Monte Carlo — Risk-Neutral GBMUSD
European Call
Terminal-value simulation benchmarked against Black-Scholes-Merton.
Delta
Simulating...
Statistical estimate unavailable
Sensitivity to one spot unit
Gamma
Simulating...
Statistical estimate unavailable
Change in Delta per spot unit
Vega
Simulating...
Statistical estimate unavailable
Sensitivity per volatility point
Theta
Simulating...
Statistical estimate unavailable
Sensitivity per calendar day
Rho
Simulating...
Statistical estimate unavailable
Sensitivity per rate point
Statistical Diagnostics
Precision and reproducibility metadata for the latest completed run
Confidence Interval
Unavailable
Two-sided normal interval
Sample Standard Deviation
Unavailable
Dispersion of discounted payoff samples
Standard Error
Unavailable
Estimated uncertainty of the sample mean
Number of Paths
Unavailable
Requested simulated paths
Effective Samples
Unavailable
Independent observations used for uncertainty
Time Steps
Unavailable
Monitoring intervals
Seed
Unavailable
Replay identifier
Computation Time
Unavailable
Plain sampling
Analytical Validation
Monte Carlo estimate compared with Black-Scholes-Merton
Analytical Price
Unavailable
Absolute Difference
Unavailable
Difference in Standard Errors
Unavailable
Absolute difference divided by Monte Carlo SE
Monte Carlo returns a statistical estimate, not an exact value. The confidence interval quantifies sampling uncertainty under the model.
European options use the exact terminal GBM distribution, so one time step is sufficient.