Julien Guyon, Professor of Applied Mathematics at ENPC, Institut Polytechnique de Paris, explains his research and findings in reconciling the P model and Q model.
Past asset returns can be connected to implied volatilities and future realized volatilities, revealing a surprising and strong link. Julien discusses an empirical study with co-author Jordan Lekeufack that demonstrates the path dependent volatility model's effectiveness and explains why using past asset prices and today’s option prices is important in generating realistic future scenarios for risk management.
Understanding path dependent volatility
Path dependent volatility leverages the historical performance of assets to provide insights into future market behaviour, creating models that capture the intricate dynamics of spot volatility. Surprisingly, these models suggest a strong relationship between past returns and future volatilities – a link that traditional finance theories hadn't fully explored.
This approach has practical applications, allowing investors and analysts to price options and hedge derivatives with greater accuracy. By utilising past asset returns, these models generate realistic predictions of market movements, aiding in the creation of strategies for statistical arbitrage and more.
Calibrating the model: A dual approach
Julien further delves into the mechanics of calibrating these models, explaining the dual sources of information involved. On one side, there’s the econometric view, which considers historical asset prices. On the other, there’s calibration based on the current prices of options – a common practice within the derivatives industry.
Historical option prices and VIX data also strengthen the calibration process, meaning that the models reflect the complex interplay between asset prices and their derivatives over time better.
Reconciling two worlds of finance
The path dependent volatility model reconciles the p calibration, which examines past asset prices, and q calibration, focusing on current option prices. Typically seen as distinct areas, Julien argues for their integration to provide a more cohesive framework for financial analysis.
This reconciliation offers profound implications for developing statistical arbitrage strategies, enabling investors to identify and exploit discrepancies between model-based and market-based prices. For institutions like banks and insurance companies, this approach facilitates more accurate stress testing and risk management, paving the way for more resilient financial planning.
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