Theta decay calculator

How this is calculated

No hidden model and nothing fitted to data. Every figure on this page comes out of these lines, applied to the numbers you typed.

t          = days ÷ 365,  σ = the volatility you enter
d1         = [ ln(S ÷ K) + ( r + σ² ÷ 2 ) × t ] ÷ ( σ × √t )
d2         = d1 − σ × √t
call       = S × N(d1) − K × e^(−r t) × N(d2)
put        = K × e^(−r t) × N(−d2) − S × N(−d1)
time value = model value − intrinsic value
theta/day  = change in model value per calendar day

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Frequently asked questions

What is theta decay?

Theta is how much an option's value changes as one day passes with nothing else moving. Part of an option's price is intrinsic value — what it would be worth exercised now — and the rest is time value, the allowance for what might still happen before expiry. Time value falls to zero at expiry, and theta is the rate at which it gets there.

Why does time decay speed up near expiry?

Because an at-the-money option's time value scales with the square root of the time left rather than with the time itself. Halving the days left does not halve the time value; it cuts it by about 29%. Half the time value is still there with a quarter of the time remaining, and then the rest goes in a rush. The chart and the half-life figure show that shape for the strike you entered.

Is the model value what the option will trade at?

No. It is what the Black-Scholes model gives for the volatility you typed, holding the underlying still. A real option's price also moves with the underlying every day, with implied volatility, with dividends and with supply and demand, so its path will not be the smooth curve drawn here. The chart isolates one force — the passage of time — and that is the only thing it claims to show.

Why do strikes far from the price decay differently?

Time value is largest at the strike and thins out with distance from it. A far out-of-the-money option has little time value and loses it relatively early, because the chance of reaching the strike fades steadily; an at-the-money option holds its time value longest and loses it fastest at the end. Distance is what matters, not side: an in-the-money strike carries nearly the same time value as an out-of-the-money one equally far away. The comparison chart puts three distances on one scale, each starting at 100.

Does this work for American-style options?

Approximately. Black-Scholes values a European option, which can only be exercised at expiry. For a call on a stock paying no dividend the two are worth the same; for a put, or a call ahead of a dividend, early exercise can make the American option worth somewhat more. The calculator notes when a European put sits below intrinsic value, which an American put would not.

Is my data sent anywhere?

No. The model runs in your browser as JavaScript on this page. Prices, strikes and volatilities are never transmitted, never stored and never logged, and closing the tab discards them. A free account unlocks the calculator; it does not send anyone your numbers.