Calibrating Stochastic Volatility Models to Historical Data

Summary

The document asks how stochastic-volatility models, particularly SABR, can be calibrated under the historical measure for long-horizon exposure simulations. It focuses on counterparty credit risk and economic scenario generation, where simulations may need to represent real-world risk-factor behavior rather than reproduce market prices under the risk-neutral measure. The author proposes fitting model parameters separately each day and then modeling their resulting time series statistically.

The text raises a further practical question: whether these applications typically use historical calibration or risk-neutral calibration. It offers no answer, calibration results, or consensus, so it serves as a research question rather than a worked method. Its central distinction is between calibrating to historical dynamics for scenario generation and calibrating to market-implied prices; the appropriate choice depends on the intended simulation use and is left unresolved here.

Key ideas

• Historical-measure calibration is relevant when simulations aim to represent real-world risk-factor dynamics over long horizons.
• SABR is raised as an example of a stochastic-volatility model whose parameters might be estimated from historical data.
• One proposed workflow is to estimate parameters by date and then model the parameter time series statistically.
• The document asks whether exposure simulation applications instead rely on risk-neutral calibration.
• No consensus, calibration procedure, or empirical comparison is provided.

Tags

# Stochastic Volatility Models Real World Calibration


# Stochastic Volatility Models Real World Calibration












I am trying to find some research pertaining to the historical (or real world) calibration of stochastic volatility models.

For example, in applications such as counterparty credit risk (IMM) or economic scenario generators (ESG), it is not unusual to simulate under the historical measure to generate exposures of various risk factors.

It is also clear that the properties exhibited by stochastic volatility models are particularly interesting for long horizon simulation.

I would like to know how one would calibrate the SABR model for example to historical data? I would assume that the model would be fitted independently for each day and the resulting time series of parameters would be fitted with a statistical model.

Finally, what is the consensus (If any) for the applications mentioned above (namely IMM and ESG): do people use the risk neutral calibration instead ?

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