Option Theta (Black-Scholes)
Computes the theta of a European call option under Black-Scholes, the Greek that measures how much premium the option bleeds with each unit of time that passes. The formula pairs the decay of extrinsic value, −S·φ(d1)·σ/(2√T), with the strike-discount effect, −r·K·e^(−rT)·N(d2). For a call with no dividends theta is always negative: time works against the buyer. The result comes as annual theta and per day (÷365). Enter the spot price, the strike, the interest rate, the term in years and the volatility.
Result
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Option Theta (Black-Scholes)
Computes the theta of a European call option under Black-Scholes, the Greek that measures how much premium the option bleeds with each unit of time that passes. The formula pairs the decay of extrinsic value, −S·φ(d1)·σ/(2√T), with the strike-discount effect, −r·K·e^(−rT)·N(d2). For a call with no dividends theta is always negative: time works against the buyer. The result comes as annual theta and per day (÷365). Enter the spot price, the strike, the interest rate, the term in years and the volatility.
What it costs to hold an option overnight
Every option you buy loses a little value simply because time has passed, even if nothing else in the market moves. That bleed has a name: theta. It's the Greek that measures how fast the extrinsic value evaporates as expiry draws closer. For the buyer, theta is the daily rent you pay on the bet.
The calculation pairs two pieces: the decay tied to volatility and the strike-discount effect. On a call with no dividends both pull downward, so theta is always negative. The clock works against the buyer and in favour of whoever sold the option. The nearer to expiry and the closer to the money, the faster that erosion runs.
The tool returns annual theta and the per-day version, divided by 365, which is the reading traders usually watch on screen. Fill in spot price, strike, interest rate, term in years and volatility. Remember it's an instantaneous sensitivity: it holds for right now and shifts as the market moves.
Related Tools
Option Veta (Vega Decay)
Computes the veta of an option, the Greek that measures how much the vega changes with each passing day. Since vega captures the premium's sensitivity to volatility, veta shows whether that sensitivity is shrinking over time, and it does: near expiry vega tends to zero, so a call's veta is usually negative. It's a second-order Greek that helps anticipate how the volatility exposure will behave. The result comes per year and per day, for a call with no dividends. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
Option Color (Gamma Decay)
Computes the color of an option, the third-order Greek that shows how much the gamma changes with each passing day, all else equal. Since gamma measures how fast the delta moves, color tells you whether that speed is accelerating or slowing as expiry approaches, handy for anyone managing gamma positions near the exercise date, where an at-the-money option's gamma spikes. The result comes per year and per day, computed for a call with no dividends. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
Option Charm (Delta Decay)
Computes the charm of an option, also known as delta decay, which shows how much the delta shifts with each passing day, all else equal. It is a second-order Greek (∂delta/∂time) that traders watch to see how a hedge needs to be rebalanced near expiry, where it spikes. For a call with no dividends it is −φ(d1)·(2rT − d2·σ√T)/(2T·σ√T). The result comes per year and per day. Enter the spot price, the strike, the interest rate, the term in years and the volatility.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.