A Factor Structure for Implied Volatility

Arbitrage Pricing Theory for Idiosyncratic Variance Factors

“…A natural question is how our APT for squared returns extends of other nonlinear transformations of excess returns. One important example would be the factor pricing of put and call options, as an alternative to the analyses in Kadan, Liu, and Tang (2017) and Christoffersen, Fournier, and Jacobs (2018). For these securities, our framework would link the factor structure in option returns to non-linear transformations of the factors that explain the cross section of returns of the underlying assets.…”

“…Conceptually the same machinery may be used to find the (non-linear) factor structure implied by other transformations, for example, it may be applied to option prices leading to an induced (again, non-linear) factor model for the cross section of option prices. Both Kadan, Liu, and Tang (2017) and Christoffersen, Fournier, and Jacobs (2018) analyze this factor structure of option prices using alternative frameworks. We follow a route based on our APT for squared returns and use option prices to identify empirically the price of these squared returns.…”

“…Our paper is related to the literature on the factor structure in option prices, for example, Kadan, Liu, and Tang (2017) and Christoffersen, Fournier, and Jacobs (2018). These papers study a direct factor structure in option prices/returns, while we follow a different route.…”