Theta

What is theta in options?

Theta is the option Greek that measures the change in an option’s theoretical value as time passes, holding the underlying price, implied volatility, and other pricing inputs constant. It is quoted per share per day: a daily theta of −0.08 per share is $8 of time decay on a standard 100-share contract.

The sign gives the direction. Negative theta lowers the long option’s theoretical value as time passes. Positive theta raises it. Selling that option reverses the position exposure.

How to calculate theta for a position

Multiply each option’s quoted theta by the contract multiplier and quantity, apply the long or short sign, and add the legs. For a long call with theta −0.08 and a short call whose long-option theta is −0.05, one contract of each gives net theta of (−0.08 + 0.05) × 100 = −$3 per day.

Use the same daily convention for both legs. A trading-day theta divides the year’s decay over fewer days than a calendar-day theta, so it prints a larger figure for the same option.

Is theta always negative for long options?

Long options carry negative theta wherever time value dominates the price, as it does near the money. Deep in the money, rates, dividends, and exercise style decide the sign.

A European put with spot $50, strike $100, six months remaining, 20% volatility, a 5% rate, and no dividends has Black-Scholes theta of +0.0134 per share per calendar day. The long contract gains $1.34 a day from the time effect, because its discounted strike value grows as expiration approaches.

How traders use theta with gamma and vega

Near expiration, at-the-money options combine rapid time decay with high gamma. Evaluate the time contribution alongside the change in directional exposure as the underlying moves. Then use vega to measure the effect of an IV change.

For a calendar or diagonal, calculate the net exposure from both expirations. For a vertical, evaluate the Greeks at the price levels in the plan. Whatever the structure is called, add the Greeks leg by leg.

Compare the expected holding period with the timing of the catalyst, then reprice the position across the dates, underlying prices, and volatility levels that matter in the options profit calculator.

Limitations of theta

• Read the day’s P&L through all the Greeks. Theta holds every other input fixed, but on a real day the underlying and implied volatility move too, and delta and vega can more than offset the $8 of decay.
• Reprice across the days you plan to hold. Theta is a local, instantaneous rate, and for an at-the-money option near expiration decay accelerates, so a week costs more than five times today’s theta.
• Match the daily convention before you compare or add thetas: a trading-day theta prints a larger figure than a calendar-day theta for the same option.
• Check the sign on deep in-the-money contracts. Rates, dividends, and exercise style can make a long option’s theta positive, as the European put’s +0.0134 a day shows.
• Price the gamma before you collect the theta. Theta describes only time, and the near-expiration at-the-money options that decay fastest also carry high gamma.

Bottom line

Theta puts a daily dollar figure on time decay: multiply the per-share quote by the contract multiplier (100 for a standard contract) and the signed quantity, then sum the legs. Use it to price the holding period against the catalyst, and read it beside gamma and vega, because a quiet day and a fast move produce very different results from the same theta.