Accounting for Earnings Announcements in the Pricing of Equity Options

Abstract

We study an option pricing framework that accounts for the price impact of an earnings announcement (EA), and analyze the behavior of the implied volatility surface prior to the event. On each known announcement date, we introduce a random jump to the stock price. Applying this idea to extend the Black-Scholes model, we obtain formulas for the pre-EA European option price, its implied volatility and various Greeks. We further incorporate random-time jumps in the stock price by extending the Kou jump-diffusion model to incorporate an EA jump, and provide an analytic option pricing formula. Moreover, we derive analytic bounds and asymptotics for the pre-EA implied volatility under various models. The calibration results demonstrate adequate fit of the entire IV surface prior to an announcement. We also compare the risk-neutral distribution of the EA jump to its historical distribution. Finally, we discuss the valuation and exercise strategy of pre-EA American options, and illustrate an analytical approximation and numerical results.