Theta

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Theta estimates how much value an option loses each day from the passage of time alone, with the stock price and implied volatility held constant. An option showing a theta of −0.05 is expected to be worth about five cents per share less tomorrow — $5 per contract — if nothing else changes.

Options decay because part of their price pays for time: more days means more chances for the stock to reach the strike. Every day that passes removes some of that possibility, and the option's time value erodes with it.

Decay is not a straight line. An at-the-money option loses value slowly early in its life and quickly near expiration, which is why short-dated options display large thetas relative to their price.

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Consider a stock at $100 and a 30-day $100 call priced at $3.00 with a theta of −0.05. Tomorrow, if the stock has not moved and implied volatility is unchanged, the model expects the call to be worth about $2.95. The entire $3.00 is time value — the option has no intrinsic value at this strike — and theta is the daily toll on it.

Roll the calendar forward. With 5 days left, the same at-the-money call might be worth $1.20 with a theta of −0.12. Less premium remains, yet the daily decay has more than doubled: at-the-money decay accelerates as expiration nears. Deep in-the-money options behave differently — a $70-strike call on the same stock is nearly all intrinsic value, leaves little time value to erode, and shows a small theta.

The all-else-equal clause carries weight. On any given day an option's actual price change is usually dominated by the stock moving or by implied volatility repricing; theta is the drift underneath that noise, not a schedule the price follows. The split between intrinsic and time value is covered under premium.

Conventions differ across platforms — some quote theta per calendar day, others per trading day — so the same option can display different figures on different sites. Options Band passes through the values from Cboe's delayed feed.

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Theta is the partial derivative of option value with respect to the passage of time, conventionally quoted per day.

Θ = ∂V/∂t

For long option positions theta is almost always negative, but not by definition. A deep in-the-money European put can carry positive theta: its value today is held below intrinsic value by discounting and rises toward the full intrinsic amount as expiration nears. Deep in-the-money calls on high-dividend stocks can behave similarly.

A common misconception treats theta as income that option sellers simply collect. Theta is an all-else-equal model sensitivity, and the position that earns decay is short gamma: on days when the stock moves more than the decay covered, the advantage runs the other way. Over time, realized profit and loss reflects the running contest between movement and decay, not theta alone.

Theta also interacts with the volatility surface. It is computed holding implied volatility fixed, while in practice short-dated implied volatility often rises into scheduled events, offsetting or masking the decay the model expects.