Derivatives · Core
Theta
Theta is the sensitivity of option value to the passing of time — the daily rent of holding convexity.
Definition
Θ = ∂V/∂t, usually quoted as value lost per day if nothing else moves. Long options pay theta; short options earn it. Weekends and event days are lumpy. Theta and gamma are twins in the Black-Scholes PDE.
Why it matters
Carry of a long-vol book is theta. If realized does not pay you, theta is the leak.
Case
A week of quiet into OPEX: short premium prints theta every day. One jump wipes four days. The carry was not free.
How to read it
Annualize theta versus the vega you are running. If carry looks amazing, you are probably short a jump.
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