The implied volatility surface describes the dependence of options prices on their moneyness (volatility smiles) and maturity characteristics (volatility term structure). This paper presents an empirical study of the factors determining the implied volatility surface for equity options. The first group of factors originates from the features of the stochastic process for the price of the underlying asset. Central to the problem of option valuation is the average quadratic variation, and, more specifically, its continuous and jump components. The evolution of an underlying’s asset price is due to continuous dynamics and jump activity.
Both components contribute to total quadratic variation, but have different implications for derivatives markets. Due to stochasticity of volatility and jump activity, investor expectations of continuous and jump components of quadratic variation influence option prices. Apart from the characteristics of the stochastic process for the underlying asset, demand and supply imbalances impact equilibrium prices. These imbalances result from the combination of three aspects of derivatives markets. First, investors are heterogeneous in terms of their market goals and risk attitudes.
Crucially, certain types of investors constitute most of the demand for options with specific strike and maturity characteristics. Second, the supply of options is imperfectly elastic due to limited interest for taking the opposite side of the trade and riskiness of options manufacturing. Finally, insufficient presence of relative value arbitrageurs prevents the market convergence to consensus expectations.
Contributing to the empirical research on derivatives markets, I provide an econometric analysis of the option pricing factors, which correspond to the features of the stochastic process for the evolution of the underlying asset. In agreement with the local volatility modeling approach of Derman and Kani (1994), conditional expectations of the continuous component of quadratic variation significantly impact short maturity option prices. In turn, volatility of volatility is fundamental to explaining prices of long maturity options. Contrary to the prediction of the Heston-type stochastic volatility models, the implied volatility skew due to randomness of the diffusion coefficient is increasing with maturity. Finally, I obtain evidence that investors systematically discount expected jump-related volatility more than volatility originating from continuous dynamics of the underlying asset.
Heterogeneity of investors is currently outside the scope of option pricing models, which implicitly assume a representative agent embodying the consensus expectations of all market participants. Building on existing option valuation models, I suggest a theoretical framework for integrating the impact of investor heterogeneity into option prices. Risk attitudes of investors uniquely determine their expectations about the arbitrage-free dynamics of the underlying asset. In incomplete markets with many admissible arbitrage-free prices for the same asset, isolated groups of investors with varying market goals and risk aversion select different risk-neutral probability measures for pricing options. This causes market segmentation simultaneous presence of multiple risk-neutral probability measures on one derivatives market. While there is recognition of the demand imbalances in options markets, the concept of market segmentation is novel and represents an attempt to extend the use of existing option pricing theory into markets with heterogeneous investors. Market segmentation presents a plausible explanation for the observed term structure of jump-related implied volatility skews and an increasing with-maturity impact of stochastic volatility on the implied volatility skew.
