Theta — Time Decay's Exact Mechanics
How fast the convex curve sags toward the kinked payoff
Time is the one input to an option's price that is guaranteed to move in only one direction. Stock prices can rise or fall; volatility can expand or contract; rates can drift either way. Time only goes down.
Every day a long-options position ages, the contract loses value purely from the calendar advancing — even if the stock and volatility are perfectly stationary. Theta is the precise dollar measure of that daily bleed. For the buyer of an option, Theta is the rent paid each day for the right to hold a convex contract.
For the seller, Theta is the daily yield earned for assuming concavity. Both sides know the rate exactly when the trade is initiated — the closed-form Black-Scholes formula gives Theta as a number of dollars per day, sometimes per day per share, sometimes per contract, depending on which scaling convention the platform uses.
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What this lesson covers
- 1Why Theta accelerates as expiration approaches
- 2Theta is highest at-the-money and decays toward zero deep ITM and deep OTM
- 3Theta in closed form (BSM)
- 4Theta evolution as a 30-day ATM call ages
- 5Why some hedge funds run 'Theta-positive' books as a discipline
- 6Where to see this on the platform
- 7Summary