Date Published: April 12, 2019
Publisher: Public Library of Science
Author(s): Jianlei Han, Martina Linnenluecke, Zhangxin Liu, Zheyao Pan, Tom Smith, Petre Caraiani.
This paper provides a general equilibrium approach to pricing volatility. Existing models (e.g., ARCH/GARCH, stochastic volatility) take a statistical approach to estimating volatility, volatility indices (e.g., CBOE VIX) use a weighted combination of options, and utility based models assume a specific type of preferences. In contrast we treat volatility as an asset and price it using the general equilibrium state pricing framework. Our results show that the general equilibrium volatility method developed in this paper provides superior forecasting ability for realized volatility and serves as an effective fear gauge. We demonstrate the flexibility and generality of our approach by pricing downside risk and upside opportunity. Finally, we show that the superior forecasting ability of our approach generates significant economic value through volatility timing.
Volatility modelling has proceeded as a field separate from asset pricing. Statistical models, such as ARCH [1, 2], GARCH , stochastic volatility , and option prices  are commonly used to estimate volatility, without reference to modern asset pricing theory. In this paper, we propose to price volatility using a general equilibrium asset-pricing framework. The advantage of such an approach is that volatility can be priced and measured in the most general setting available. The approach also allows us to extend measurement and pricing (such as downside risk pricing and upside opportunity pricing), which cannot be achieved with current approaches to volatility modelling.
This paper is novel in that it proposes a general equilibrium framework to price volatility in the same manner as is the case for all securities in the market, following Arrow and Debreu . Using state prices estimated from S&P 500 index options, we illustrate how we can derive ex-ante volatility measures SVXI for industry portfolios, in which there are no traded options. The SVXI measures generate superior forecasting abilities for the future realized volatility and serve as qualified fear gauges. We show that our approach is flexible and general by extending it to downside risk and upside opportunity. Finally, we demonstrate that the superior forecasting ability of our general equilibrium volatility measure can create significant economic value through a simple volatility timing strategy. Our findings, together with the fact that the industry volatility indices can be easily constructed under the general equilibrium framework, offer practitioners an appealing alternative tool for managing volatility. Our general equilibrium framework is not limited to pricing volatility, but can be applied to price any moments of the return distribution.