This paper investigates Black-Scholes call and put option thetas, and derives upper- and lower-bounds for thetas as a function of underlying asset value. It is well known that the maximum time premium of an option occurs when the value of the underlying asset equals the exercise price. However, we show that the maximum option theta does not occur at that point, but instead occurs when the underlying asset’s value is somewhat above the exercise price. We also show that option theta is not monotonic in any of the parameters in the Black-Scholes option-pricing model, including time to maturity. Finally, we explain why the implications of these findings are especially important for trading and hedging strategies that are affected by the decay in an option’s time premium.