Computationally Efficient Multi-Asset Stochastic Volatility Modeling

Abstract

Stochastic volatility (SV) models are popular in financial modeling, because they capture the inherent uncertainty of the asset volatility. Since assets are observed to co-move together, multi-asset SV (mSV) models are more appealing than combining single-asset SV models in portfolio analysis and risk management. However, the latent volatility process renders the observed data likelihood intractable. Therefore, parameter inference typically requires computationally intensive methods to integrate the latent volatilities out, so that it is computationally challenging to estimate the model parameters.

This three-part thesis is concerned with mSV modeling that is both conceptually and computationally scalable to large financial portfolios. In Part I, we explore the potential of substituting the latent volatility by an observable market proxy. For more than 20 years of out-of-sample predictions, we find that modeling the Standard and Poor's 500 (SPX) index by a simple framework of Seemingly Unrelated Regressions (SUR) with VIX volatility proxy is comparable to the benchmark Heston model with latent volatility, at a fraction of the computational cost.

In Part II, we propose a new mSV model structured around a common volatility factor, which also can be proxied by an observable process. Unlike existing mSV models, the number of parameters in ours scales linearly instead of quadratically in the number of assets -- a desirable property for parameter inference of high-dimensional portfolios. Empirical evidence suggests that the common-factor volatility structure has considerable benefits for option pricing compared to a richer class of unconstrained models.

In Part III, we propose an approximate method of parameter inference for mSV models based on the Kalman filter. A large-scale simulation study indicates that the approximation is orders of magnitude faster than exact inference methods, while retaining comparable accuracy.