Equity index variance: Evidence from flexible parametric jump–diffusion models

Abstract

This paper analyzes a wide range of flexible drift and diffusion specifications of stochastic-volatility jump-diffusion models for daily S&P 500 index returns. We find that model performance is driven almost exclusively by the specification of the diffusion component whereas the drift specifications is of second-order importance. Further, the variance dynamics of non-affine models resemble popular non-parametric high-frequency estimates of variance, and their outperformance is mainly accumulated during turbulent market regimes. Finally, we show that jump diffusion models yield more reliable estimates for the expected return of variance swap contracts.

Inferring information from the S&P 500, CBOE VIX, and CBOE SKEW indices

“…In this paper, we consider three typical models. The first model is the stochastic volatility model with contemporaneous jumps in returns and volatility (SVCJ), which is the most popular affine model in the literature, for example, Bakshi, Cao, and Chen (1997); Broadie, Chernov, and Johannes (2007); Da Fonseca and Ignatieva (2019); Duan and Yeh (2010); Eraker (2004); Eraker, Johannes, and Polson (2003); Kaeck, Rodrigues, and Seeger (2017); Lin and Chang (2010); Neuberger (2012); Neumann, Prokopczuk, and Simen (2016); Ruan and Zhang (2018); Zhu and Lian (2011, 2012); and others. Bakshi et al (1997), Broadie et al (2007), Eraker (2004), and Neumann et al (2016) document that the SVCJ model is good enough to fit options and returns data simultaneously.…”

Model risk in the over-the-counter market

“…Adding Poisson jumps in the return process of SV (which gives the SVJ model) slightly reduces the MSpR, while adding variance-gamma jumps in the return process of SV (which is SVVG) increases it. Further adding Poisson jumps in the variance process of SVJ (SVCJ) yields a much lower MSpR, 11.49, in estimating VS rates Kaeck et al (2017). also find that jump diffusion models yield more reliable estimates of the VS rates.…”