What problem does it solve? Estimating the probability of binary events like "Will AAPL close above $200?" requires rigorous statistical simulation rather than guesswork. This Skill provides the foundational Monte Carlo methods for pricing binary contracts, quantifying estimation uncertainty with confidence intervals, and measuring forecast calibration. ## Core Features & Use Cases - GBM Path Simulation: Simulates terminal asset prices under Geometric Brownian Motion to estimate binary payoff probabilities with standard errors and 95% confidence intervals. - Sample Size Planning: Computes required path counts for target precision using CLT convergence rates, accounting for maximum variance at p = 0.5. - Brier Score Calibration: Evaluates forecast quality against benchmarks (below 0.20 good, below 0.10 excellent) to compare model sharpness. - Use Case: A prediction market analyst wants to price a contract on AAPL exceeding $200 in 30 days. Provide current price, drift, volatility, and time to expiry to get a probability estimate with confidence bounds. ## Quick Start Ask the agent to simulate the probability of AAPL closing above $200 in 30 days given 20% volatility and 8% drift using Monte Carlo simulation.
