Modeling Implied Volatility Surfaces in Options Backtests

Summary

The document proposes a Monte Carlo approach for backtesting options strategies that models underlying prices and the implied volatility surface as separate, potentially correlated sources of uncertainty. It suggests generating price paths with a Heston model calibrated under the real-world measure, then applying principal component analysis to an SVI surface parameterization and fitting stochastic processes to the resulting components. Those simulated components would be used to reconstruct future volatility surfaces and reprice options along the paths.

The proposal is motivated by the view that deriving implied volatility directly from a Heston model may miss the dynamics of the observed volatility surface. However, the document presents this as a question for feedback, not a tested method: it gives no empirical comparison, calibration details, or backtest results. It also leaves open how to model dependence between price moves and surface changes, and whether the added surface simulation is necessary for a particular strategy or horizon.

Key ideas

• The proposed backtest simulates underlying prices with a real-world calibrated Heston model.
• It models implied volatility surface changes through principal components of an SVI parameterization.
• The simulated surface components are intended to be correlated with price paths.
• The document questions whether deriving implied volatility directly from Heston captures enough surface dynamics.
• The proposal is exploratory and supplies no empirical results or implementation details.

Tags

# MC Backtesting for Options


# MC Backtesting for Options












I'd like to get your feedback on how you would approach Monte Carlo simulation to backtest some options strategies. My main concern is about how to model the dynamics of the implied volatility (IV) surface — and whether you think it's even relevant to do so.

So far, I've considered the following approach:

- Use a Heston model (calibrated under the real-world measure) to generate random price paths

- Apply PCA to the SVI parameterization of the IV surface, fit a stochastic process to each principal component, and use this to generate random paths (correlated with the Heston-generated price paths)

- Reconstruct the IV surface and reprice accordingly

To me, this method seems more realistic than the more common approach I often see, which combines Heston (sometimes under Q) with the assumption that IV equals the volatility directly derived from the Heston model.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.