Theta and Time Decay in Options Trading
Jun 27, 2023
Option theta, or the first derivative of the Black-Scholes option pricing model with respect to time, measures how an option price changes with each passing day. In other words, option theta puts a monetary value on each calendar day.
Options differ from stock in that all options have a fixed end point, also referred to as their expiration dates. At expiration, the extrinsic value of each option contract must equal zero, and as time passes and the options contract gets closer to expiration, this extrinsic value will slowly decrease—a phenomenon commonly referred to as time decay.
Mathematically, it might also be useful to know that option theta is not a linear function. It does not remain constant over time, causing the same amount of extrinsic value to fall off the option each day. Instead, option theta is a nonlinear and changes from day-to-day. Its specific value and magnitude are largely determined by just how much time is left in the cycle and whether the contract is in-the-money, at-the-money or out-of-the-money.
We want to familiarize ourselves with two fundamental principles of option theta now that we have a mathematical foundation in place. First, option theta is always presented in actual dollars, given its monetary relationship to each day. For instance, an option theta of “0.03” can be directly converted into $0.03 because that number shows the amount of option theta per share, per day.
Given that a standard option contract is for 100 shares, the total theta of the position would be $0.03 per share over 100 shares in the contract, for a position theta of $3. Note that in the world of options, option theta is almost always referenced in its total contract value. So, an option theta of $0.03 per share or $3 per contract, is universally referred to as a theta of “3.”
Lastly, option theta is not the same for option buyers and option sellers. In fact, one side of the contract is directly opposed to the other side. Options buyers always have negative option theta, and options sellers always have positive option theta. The reason for this derives from the relationship we noted earlier between option theta and extrinsic value. Options buyers want options prices to rise, so the slow decay of extrinsic value works against them. Hence, you have negative option theta. Conversely, options sellers want options prices to fall, so the slow decay of extrinsic value works for them and, hence, they have positive option theta.
Jim Schultz, a quantitative expert and finance Ph.D., has been trading the markets for nearly two decades and hosts From Theory to Practice, Monday-Friday on tastylive. He breaks down the mathematical relationships in the derivatives market and shows how to retail portfolios.
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