Trading Options in Turbulent Markets: Master Uncertainty through Active Volatility Management

Chapter 8. Sand in the Hourglass: Volatility and Option Theta

Theta, otherwise known as time decay, is an approximation that measures how quickly time value disappears from an option with the passing of one day without movement in either the underlying asset or implied volatility. Specifically, theta is used to approximate how much an option's extrinsic value is carved away by the passage of time. The theta for a call and put at the same strike price and the same time to expiration is generally similar but not exactly equal.

The difference in theta between calls and puts solely depends on the individual stock's cost of carry. Thus, an underlying asset without a dividend or a dividend yield that is implied (i.e., stock index future) will have call and put thetas that are equal. When the cost of carry for a stock is positive (i.e., dividend yield is less than the interest rate), theta for the call is higher than theta for the put. When the cost of carry for the stock is negative (i.e., dividend yield is greater than the interest rate), theta for the call is lower than that for the put (see Exhibit 8.1).

Long options always have negative theta. Short options always have positive theta. An underlying asset, whether you are long or short, has zero theta (see Exhibit 8.2). In other words, its value is not eroded by time. Theta causes an option with more time to expiration to have additional extrinsic value as compared with an option with fewer days remaining to expiry. Thus, it should make ...