01
TRADITIONAL MONTE CARLO
Reliable but computationally expensive
VS
02
PREDICTION-ENHANCED MC
ML-enhanced with 30-55% variance reduction

ASIAN OPTION PARAMETERS

SIMULATION PARAMETERS

RESEARCH PAPER

Prediction-Enhanced Monte Carlo
A Machine Learning View on Control Variate
Li et al. (2024)
arXiv:2412.11257v3
30-55% RMSE Reduction Production-Grade
DOWNLOAD PAPER
↓

PEMC FORMULA

PEMC Estimator:
PEMC = (1/n)Σ[f(Yi) - g(Xi)] + (1/N)Σ[g(X̃j)]
Unbiased estimation with proven variance reduction

PRICING COMPARISON

MC
Monte Carlo
$1.8542
Standard Error: ±0.0156
Samples Used: 10,000
Computation Time: 2.34s
PEMC
Enhanced MC
$1.8567
Standard Error: ±0.0089
Total Samples: 11,000
Computation Time: 1.67s

PERFORMANCE METRICS

VAR
VARIANCE REDUCTION
43.2%
PEMC vs Standard MC
SPEED
EFFICIENCY GAIN
2.1x
Speed Improvement
CORR
ML CORRELATION
0.73
Prediction Quality
COST
COST RATIO
0.001
Cheap vs Expensive

CONVERGENCE ANALYSIS

KEY INSIGHTS

01

Variance Reduction

PEMC achieves 30-55% variance reduction by using ML predictions as control variates, maintaining unbiasedness while improving efficiency.

02

Computational Efficiency

By leveraging cheap ML evaluations (N=10,000) with fewer expensive simulations (n=1,000), PEMC optimizes the cost-variance tradeoff.

03

Statistical Rigor

Unlike pure ML approaches, PEMC preserves Monte Carlo's unbiasedness and provides rigorous confidence intervals for risk management.