Understanding the dynamics and economic drivers of volatility, or financial assets' price variability, is of great interest to academics and practitioners. The recent literature focuses on the variance risk premium that investors require for the well known fact that volatility is stochastic. The variation over time of the magnitude of price movements of financial assets (variance risk) represents a source of uncertainty that agents are subject to. Consistently, risk adverse agents should require a compensation for bearing the randomness of future variance. The VRP is defined as the difference between the risk neutral and physical expectations of an asset's total return variation. This project aims at formulating a class of dynamic model for the latent VRP in a joint specification for the physical variance and its option implied risk neutral expectation. We advocate the inclusion of interactions and discontinuities as being essential to replicate dynamics and interdependencies between the asset's variance and its risk neutral expectation. We aim at formulating a joint specification which is computationally feasible, does not impose a restrictive parametric structure, allows to account for error in the ex-post measurement of latent variables, accounts for interactions, non-linearities and discontinuities, and linkages with macro-finance and business-cycle variables. By exploiting the temporal causality between realizations and expectations we investigate the extent to which agents anticipate large shocks on the markets (disasters) and the way they perceive such disasters in terms of the length of their impact on the markets. We also aim at extending the analysis along two dimensions: along a pure cross-sectional dimension, to various classes of financial assets (infividual stocks, diversified porfolios and commodities) in serach of idiosyncracies/commonalities and, along the expectations horizon dimension, investigating the VRP term structure.
Due to its latent nature, the estimation of the VRP is inherently problematic. The ambiguity characterizing the empirical results available in the literature stems from the detection of spurious relationships and is largely due to a number of problems affecting the way the VRP is defined, constructed, modeled and/or estimated. We aim at providing a solution to these problems by developing a new approach to the VRP extraction that delivers more refined and realistic measures of the premium, that is able to capture more precisely the linkages with the economy and that can constitute a new benchmark to empirically validate
economic theories. Starting from a suitable representation of the market variance through an artificial variance
swap contract, our goal is to build a class of flexible structural models for financial assets return variance that aims at isolating as structural components the price attached by the market to the variance risk, i.e. the VRP, and the variance expectations under the RND. An ambitious aspect of this project is the inclusion of interactions, non-linearities and discontinuities - with emphasis on
structural brakes, regime changes, cyclical components and trends, spillovers, etc. - essential to replicate complex dynamics and interdependencies not yet explored to date. Given the latent nature of the variables of interest (the financial asset variance and its expectations under the real and the risk neutral densities), of which only imprecise approximations are observable (realized variance, options implied variance), we advocate the use of methodologies based on signal extraction techniques, see Durbin et al. (2004), that allow us to obtain measurement error free estimates of the VRP, and thus to disentangle, with a high degree of precision, its underlying time series properties as well as possible dependencies with the state of the economy. One of the challenges of this approach is the need to adapt, to an inherently complex model structure, sophisticated filtering and optimization techniques, see Durbin et al. (2012) and Zeng (2013), in a scrupulous and novel manner.
From an empirical standpoint, our objective is to carry out an extensive comparative analysis of the characteristics of the VRP and its links with the economic activity to identify commonalities and idiosyncrasies with respect to: the state of the economy (e.g., calm vs market turmoil), the size of the underlying portfolio and/or the degree of diversification, namely individual assets,
small portfolios (e.g., DJIA - 30 industry sector stocks, NASDAQ100 - 100 large technology sector stocks), large portfolios (e.g. SP500 - 500 large caps, Russell2000 - 2000 mid caps) and the economic environment (e.g., SP500, DAX, NIKKEI225, BOVESPA), as well as commodities markets (energy, agricultural, metals). To our knowledge, such comprehensive study has not been done yet.
We expect the output of this research to contribute with at least 2 scientific articles publishable in top peer-reviewed journals within finance such as Journal of Financial Economics, Review of Financial Studies or Journal of Financial Quantitative Economics.