Pricing and hedging options with rollover parameters

We implement a “horse race” competition between several option-pricing models for Standard & Poor’s 500 options. We consider trader rules (the so-called ad hoc Black–Scholes model) to predict future implied volatilities by applying simple ad hoc rules, as well as mathematically complicated option-pricing models, to the observed current implied volatility patterns. The traditional rollover strategy, ie, the nearest-to-next approach, and a new rollover strategy, the next-to-next approach, are also compared for the parameters of each option-pricing model. We find that simple trader rules dominate mathematically more sophisticated models, and that the next-to-next strategy can decrease the pricing and hedging errors of all option-pricing models, unlike the nearest-to-next approach. The “absolute smile” trader rule, which assumes that the implied volatility follows a fixed function of the strike price, has the advantage of simplicity and is the best model for pricing and hedging options.