How to Create a Volatility Risk Assessment

I really like this paper from researchers at HEC Montréal, titled Deep Implied Volatility Factor Models for Stock Options.  It elegantly solves the classic trade-off between modern machine learning and traditional financial modeling. Sam Cohen, Lukasz Szpruch, and myself have written about the benefit of these hybrid models in "Black-box model risk in finance". The computationally "heavy" part—training the neural network to learn the complex volatility shapes—is done only once. Pure machine learning models are often "black boxes," which regulators and risk managers dislike. It blends power with interpretability. 1. One-Time Training: A neural network is trained once on historical data to learn a stock's unique basis factors for volatility, including its specific pre-earnings ramp-up shape. 2. Daily Data Ingestion: Each day, ingest current market data for all traded options: their moneyness, maturity, implied volatility, and the time-to-earnings-announcement (TTEA). 3. Rapid Daily Fitting: Perform a fast daily linear regression (OLS) to calculate the factor loadings (betas) that best fit the day's observed market prices using the pre-trained basis factors. 4. Construct IV Surface: The daily betas yield a complete, smooth function for the entire IV surface, allowing for immediate and consistent pricing of any option, including non-standard strikes. 5. Derive Risk Metrics: Use the complete surface to compute advanced metrics like the stock's risk-neutral probability distribution or a custom, 30-day VIX-style index for targeted risk analysis.

Day 3 of 7: Unlocking Quant Knowledge – Monte Carlo Method for VaR Welcome to Day 3! Today, we’re taking a closer look at the Monte Carlo Method for calculating Value at Risk (VaR)—with a real-world example to show how it works in risk management. Monte Carlo Recap (Please also refer to my post on Monte Carlo from last week) Unlike simpler VaR methods that assume normal returns or ignore how stocks move together, Monte Carlo simulations generate thousands of possible market scenarios. Each scenario reflects different daily (or monthly) returns for every stock, capturing correlations and offering a more realistic view of risk. A Real-World Example: Monthly VaR for a Tech Portfolio - Defining the Portfolio Imagine you have $1 million invested across three tech-oriented stocks: Tesla (40%), Apple (35%), and Microsoft (25%). Based on historical data, Tesla has an annual volatility of 30%, Apple 20%, and Microsoft 18%. You also gather correlation data to capture how these stocks move together during major tech events. - Adjusting for a 1-Month Horizon Since you want a 1-month VaR, you scale annual volatility accordingly to reflect realistic monthly fluctuations. - Running the Simulations Your risk system generates 10,000+ random future price paths for each stock over one month. Some scenarios show minor fluctuations, while others simulate market shocks where all three stocks decline sharply. - Identifying Potential Losses After ranking the simulated portfolio losses, you identify the 95th percentile loss. If the 95% VaR is $50,000, this means there is a 5% chance of losing more than $50,000 in one month. Why This Matters Captures Correlations: If Tesla and Apple both drop after weak earnings, your model reflects this relationship, unlike simpler methods that treat stocks as independent. Accounts for Tail Risk: Standard geometric Brownian motion assumes log-normal returns, which may underestimate extreme events, but Monte Carlo can incorporate fat-tailed distributions for a more accurate risk assessment. Supports Better Decisions: Understanding potential worst-case losses helps investors decide whether to hedge, rebalance, or adjust their exposure. Key Takeaways - Monte Carlo offers a more realistic risk assessment by factoring in changing correlations, dividends, and non-normal distributions. - Reliable inputs, particularly for volatility and correlations, are essential for accurate results. - While computationally demanding, Monte Carlo provides deeper insights than simpler VaR models. Fun Fact Monte Carlo simulations were named after the Monaco casino district, highlighting their reliance on probability and randomness to predict outcomes. Follow along, share your thoughts, and let’s master VaR together—how do you see Monte Carlo clarifying your investment risks? #QuantFinance #RiskManagement #ValueAtRisk #MonteCarlo #EquityPortfolio #FinancialModeling #Finance #Inestment #MarketRisk

Day 2: Calculating VaR by using the Historical Simulation Method Using historical simulation for Value at Risk (VaR) on a multi-asset portfolio involves evaluating historical price changes for all assets in the portfolio, applying those changes to the current portfolio values, and determining the potential losses based on the confidence level. Here's a step-by-step explanation with a formula and example: Steps for Historical Simulation VaR on a Multi-Asset Portfolio 1. Collect Historical Data Gather historical price or return data for all assets in the portfolio over a specific period (e.g., 1 year of daily data). 2. Calculate Portfolio Returns for Each Day Use the historical percentage changes in the prices of individual assets to calculate the portfolio’s total return on each historical day. 3. Apply Historical Returns to Current Portfolio Value For each historical day, calculate the hypothetical portfolio value 4. Calculate Portfolio Losses Determine the loss relative to the current portfolio value 5. Rank Losses Rank all the historical losses from smallest to largest. 6. Determine the VaR Identify the loss at the desired confidence level (e.g., the 5th percentile for 95% confidence). This methodology can be extended to larger portfolios with more assets and longer time periods using similar steps, often implemented in tools like Python or R for automation. Let me know if you'd like help with coding or deeper analysis! #Quant #Risk #Riskmanagement #VaR #Marketrisk #Financialmathematics #Finance #Derivatives #Equity #Bonds #Fixedincome