Monte Carlo Simulation Engine

Advanced statistical simulation and visualization platform

Black-Scholes Monte Carlo Simulation

Stock Price (S₀)

Strike Price (K)

Volatility (σ) 20%

Risk-free Rate (r) 5%

Time to Expiry (T) - Years

Number of Simulations

Ready

Price Distribution

Convergence Plot

Results & Analysis

Call Option Price —

Put Option Price —

95% CI (Call) —

Mean Final Price —

Std Deviation —

Min Price

—

Max Price

—

Median Price

—

95th Percentile

—

5th Percentile

—

Pi Estimation via Monte Carlo

Number of Points

Animation Speed

Ready

Pi Estimation Results

Estimated π —

Actual π 3.14159

Error —

Points in Circle —

Points in Square —

Method

Random Points

Accuracy

—

Random Walk / Brownian Motion

Number of Paths

Time Steps

Drift (μ) 10%

Volatility (σ) 15%

Ready

Particle Paths

Final Position Distribution

Simulation Statistics

Mean Final Value —

Std Deviation —

Min Value —

Max Value —

Percentile 5

—

Percentile 25

—

Median

—

Percentile 75

—

Percentile 95

—

Portfolio Risk (Value-at-Risk)

Asset 1 Return (%)

Asset 1 Volatility (%)

Asset 2 Return (%)

Asset 2 Volatility (%)

Asset 3 Return (%)

Asset 3 Volatility (%)

Correlation (1-2) 30%

Correlation (1-3) 20%

Correlation (2-3) 40%

Portfolio Size

Allocation A1 (%)

Allocation A2 (%)

Ready

Loss Distribution

Cumulative Loss Distribution

Risk Metrics

Value at Risk (95%) —

Value at Risk (99%) —

Conditional VaR (95%) —

Expected Return —

Portfolio Volatility —

Sharpe Ratio —

Mean Return

—

Best Case

—

Worst Case

—