Dividend-Rollover Effect and the Ad Hoc Black-Scholes Model

Abstract

One of the most widely used option-valuation models among practitioners is the ad hoc Black-Scholes (AHBS) model. The main contribution of this study is methodological. We carefully consider three dividend strategies (No dividend, Implied-forward dividend, and Actual dividend) for the AHBS model to investigate their effect on pricing errors. We suggest a new dividend strategy, implied-forward dividend, which incorporates expectational information on dividends embedded in option prices. We demonstrate that our implied-forward dividend strategy produces more consistent estimates between in-sample market and model option prices. More importantly our new implied-forward dividend strategy makes more accurate out-of-sample forecasts for one-day or one-week ahead prices.

Second, we document that both a “Return-volatility” Smile and a “Return-pricing Error” Smile exist. From these return characteristics, we make two conclusions: (1) the return dependency of implied volatility is an important explanatory variable and should be controlled to reduce the pricing error of an AHBS model, and (2) it is important for the hedging horizon to be based on return size, that is, the larger the contemporaneous return, the more frequent an option issuer must rebalance the option’s hedge.

Keywords: Dividends, Black-Scholes, Ad hac, Implied, Volatility, IVOL, AHBS, Expectations, Forward, Hedging