Theta
Theta is how much an option's value is expected to change per day from time passing alone, with price and implied volatility unchanged; it is negative for options you own (that is the value they lose each day), and the decay accelerates as expiry approaches.
What theta measures
Part of every premium is time value: what the market charges for the chance of a bigger move before expiry (see moneyness). That part melts as the days pass, and at expiry it is zero. Theta is the daily rate of that melt: a theta of −$95 means the option loses about $95 per day if nothing else changes.
- Owning options gives negative theta: time works against you.
- Selling options gives positive theta: time works for you, which is why sellers talk of "collecting theta".
- At-the-money options have the most time value, so their theta is the most negative: they lose the most per day.
A worked example
The $100,000 BTC call with 30 days left and 50% IV is worth about $5,714 and has a theta of about −$95 per day. Repricing it with 29 days left, everything else equal, gives $5,618: $96 less. Theta is not constant, though:
- with 7 days left, the same at-the-money call loses about $197 per day;
- with 1 day left, about $522 per day.
Time decay accelerates near expiry, roughly with one over the square root of the time left. The 30-day option loses about 12% of its value in its first week; its last week takes almost half of what it was worth at 30 days.
Theta is the price of gamma
Theta and gamma come together. The option that decays fastest is the one whose delta changes fastest. A buyer pays theta every day for the right to profit from big moves; a seller is paid theta every day for accepting the losses from them. Neither side has an edge from time alone: who wins depends on how much the price actually moves against what implied volatility priced in.
Theta in strategies
Income strategies (short strangles, iron condors, covered calls) are built to collect theta while limiting or accepting the risk of a large move. Calendar spreads exploit the different speeds: the short near-dated option decays faster than the long far-dated one. On every strategy page, the "time effect" text and the structure's live theta say which side of this trade you are on.
Crypto specifics
Crypto trades every day, weekends included, so options decay over calendar days, not trading days. BOSS's theta is per calendar day, the same convention the venues use. Daily options on these venues expire at 08:00 UTC; with less than a day to go, theta is a large share of what is left of the premium.
Live on BOSS
Theta across a range of BTC prices for today's at-the-money call and put on the selected venue. The dip is deepest at the strike: that is where an option loses the most value per day. Pick a nearer expiry and the dip gets deeper.
Values above are the venue's own Greeks for one contract right now. Curves are the Black-Scholes model at each option's current implied volatility, across a range of prices; the marker is the current price.
Long Call
Long Put
Common mistakes
- Selling short-dated options for their theta without sizing for the gamma that comes with it.
- Expecting theta to be steady: an at-the-money option's daily decay multiplies several times over in its last week.
- Thinking a long option loses money only when the price goes the wrong way. Standing still costs theta every day.
- Comparing theta across options of very different prices: a cheap far OTM option has small theta in dollars but can lose a large share of its value per day.
Where this shows up on BOSS
Educational content, not investment advice. See the disclaimer.