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Theta (Θ)

Theta measures how much an option's price decreases as time passes, all else equal. Also called time decay.

Definition

Theta is the daily erosion of an option's extrinsic value. Long options bleed theta; short options collect it.

Key Properties​

Usually negative: Options lose value over time
Highest at: ATM, near expiry
Units: $ per day (or per year)

See It In Action​

Play with the calculator to see how theta decay accelerates as expiry approaches:

Theta Decay Calculator

Option Price
$6,478
ATM call
Daily Theta
-$111
per day
Last 7d Decay
$2,353
accelerated
At Expiry
$6,478
intrinsic only
$6,478$4,859$3,239$1,620$030d23d15d8d0dTodayDays to ExpiryOption Value
Strike (% of spot)100% ($100,000)
80% ITM120% OTM
Days to Expiry30 days
1 day90 days
Implied Volatility55%
20% (low)120% (high)
Key insight: Theta decay accelerates as expiry approaches. ATM options have the highest theta because they have the most time value to lose.

How Theta Works​

Every day that passes, options lose some extrinsic value. At expiry, only intrinsic value remains.

The key insight: Theta decay is not linear. It accelerates dramatically in the final days before expiry.

Theta by Position​

Position
Theta
Effect
Long call
Negative
Lose money each day
Long put
Negative
Lose money each day
Short call
Positive
Earn money each day
Short put
Positive
Earn money each day

Option buyers pay theta. Option sellers collect theta.

Theta Acceleration​

The most important thing to understand about theta: it's not constant.

Days to Expiry
Daily Decay (ATM)
Character
60+ days
Low
Barely noticeable
30 days
Moderate
Steady bleed
14 days
High
Noticeable daily
7 days
Very High
Significant daily
1-3 days
Extreme
Melting ice cube

ATM options experience the most dramatic acceleration because they have the most extrinsic value to lose.

Theta by Moneyness​

MoneynessTheta Behavior
Deep ITMLow theta - mostly intrinsic value, little to decay
ATMHighest theta - maximum extrinsic value
OTMModerate theta - all extrinsic, but less total value
Deep OTMLow absolute theta - not much value left
💡

ATM options have the highest theta because they have the most time value. But deep OTM options can lose 100% of their value if they expire worthless.

The Gamma-Theta Trade-off​

There's no free lunch in options.

💡

Long options: Negative theta but positive gamma (you pay for convexity)

Short options: Positive theta but negative gamma (you collect premium but face blow-up risk)

This is fundamental:

  • If you want the right to benefit from big moves (gamma), you pay for it daily (theta)
  • If you collect premium (theta), you take the risk of big moves hurting you (gamma)

Theta and IV​

Theta is higher when IV is higher. Why?

Higher IV means higher option prices, which means more extrinsic value to decay. A 90% IV option has more time value (and thus more theta) than a 40% IV option.

This is why post-earnings options experience dramatic decay: not just from the passage of time, but from the IV crush reducing extrinsic value.

Practical Implications​

For Buyers​

  • Don't buy short-dated options unless you have strong conviction
  • Theta works against you every day
  • The last week before expiry is brutal

For Sellers​

  • Theta is your edge... but so is gamma your risk
  • Consider selling options with 30-45 DTE to balance theta collection with gamma risk
  • Near-expiry options have high theta but unpredictable gamma moves

Weekend Decay​

Theta is usually quoted as a daily rate, but weekends exist. How do markets handle this?

Most models assume theta accrues continuously. In practice, weekend decay is often priced into Friday's close. You don't get "free" days.

On Hypercall​

Options on Hypercall expire at 08:00 UTC. Weekend decay is priced throughout the week - there's no special "weekend theta" adjustment.

For a European call option under Black-Scholes:

Θcall=−S⋅N′(d1)⋅σ2T−rKe−rTN(d2)\Theta_{\text{call}} = -\frac{S \cdot N'(d_1) \cdot \sigma}{2\sqrt{T}} - rKe^{-rT}N(d_2)

Where:

  • N′(d1)N'(d_1) is the standard normal PDF
  • The first term is the primary decay (always negative)
  • The second term relates to the risk-free rate

Key observation: Theta scales with 1T\frac{1}{\sqrt{T}}, which is why it accelerates as T→0T \to 0.

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