Approximating Multi-Factor Stochastic Volatility with One Factor

Summary

The document asks whether a multi-factor stochastic volatility model, especially a two-factor model, can be approximated by a faster single-factor model for Monte Carlo calibration. It defines the distinction in terms of the number of Brownian motions driving stochastic volatility and names a Heston-style model as a possible simpler target.

The proposed goal is to retain enough of the richer model’s volatility dynamics to reprice them accurately while reducing calibration time. The document does not provide an approximation method, a literature review, citations, or numerical evidence. It therefore frames a research problem rather than explaining a solution. Any practical use would require identifying which volatility features and instruments must be preserved, then validating the reduced model’s pricing accuracy against the original across the relevant calibration set.

Key ideas

• The document seeks a faster one-factor substitute for a multi-factor stochastic volatility model during Monte Carlo calibration.
• It defines model dimensionality by the number of Brownian motions driving stochastic volatility.
• The desired approximation should preserve the volatility behaviors needed for accurate repricing.
• No method, references, or validation results are provided.

Tags

# 73347


# Reference request: Approximate mapping of a multi-factor stochastic volatility model to single-factor stochastic volatility model












I am looking for approaches to transform a more complicated stochastic volatility model such as the one shown in Section 2.2 of Smile Dynamics II to a single-factor model such as the one shown in Section 2.1 of the same paper or some kind of version of Heston. I am interested in this question because I want to do a Monte Carlo based calibration and my model (which has multiple factors) is too slow for this. A reasonable approximation with a simpler (one-factor) model would be much faster and would be acceptable in this context.

In more detail, I am mostly interested in a one-factor approximation of two-factor stochastic volatility models, such that most of the volatility dynamics behaviours modelled by the two-factor model are accurately reprices by the one-factor one. A one factor would have a single Brownian motion driving the stochastic volatility, whereas and $n$-factor model would have $n$ Brownian motions driving the stochastic volatiity.

Have such questions been studied in the literature? Have such questions been studied in some generality or only for some types of models?

I could not find any reference until now, but I am sure there must be such approaches out there.

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