Risk Models: Parametric, Historical, and Monte Carlo

Module: Fintech AI | Difficulty: Advanced

Parametric VaR

Historical VaR

Monte Carlo VaR

Comparison

| Method | Assumptions | Speed | Accuracy | |--------|------------|-------|----------| | Parametric | Normal | Fast | Low | | Historical | Stationary | Medium | Medium | | Monte Carlo | Model | Slow | High |

import numpy as np

class VaRCalculator:
    def __init__(self, confidence=0.99):
        self.alpha = confidence
    def parametric_var(self, returns):
        mu, sigma = returns.mean(), returns.std()
        z = -2.326  # 99% confidence
        return -(mu + sigma * z)
    def historical_var(self, returns):
        return -np.percentile(returns, (1-self.alpha)*100)
    def monte_carlo_var(self, returns, n_sims=10000):
        mu, sigma = returns.mean(), returns.std()
        simulated = np.random.normal(mu, sigma, n_sims)
        return -np.percentile(simulated, (1-self.alpha)*100)
    def expected_shortfall(self, returns):
        var = self.historical_var(returns)
        return -returns[returns <= -var].mean()

Research Insight: Each VaR method has strengths and weaknesses. Parametric is fast but assumes normality. Historical is model-free but assumes stationarity. Monte Carlo is flexible but requires a model. The best practice is to use multiple methods and compare results.