Theta decay, measured on 19 years of real SPY quotes: ATM extrinsic dies ~2× faster than theo
None of this is new or novel, I'm posting this moreso for newer traders to get a feel for some of the more nuanced relationships between theoretical pricing and markets.
- Data: end-of-day SPY option chains, Jan 2007 → Jul 2026, marked at bid/ask **mid**.
- For every SPY expiration, on the first trading day with 43–46 DTE I "select" three structures at that day's chain: the ATM straddle (strike nearest spot), the 25Δ strangle, and the 10Δ strangle (strikes nearest those deltas). Entry requires live bids on every leg.
- I then track those **exact fixed strikes** every day to expiration and compute **extrinsic (time) value** = mid − intrinsic at that day's spot.
- Each path is normalized by its entry extrinsic; the curves below are the **median across all 796 qualifying expirations**, with interquartile bands on the chart.
- 796 expirations = every monthly plus every weekly that had quotes ~45 days out.
**The ATM curve is nothing like the textbook.**
By 21 DTE the median real ATM straddle has lost 71% of its extrinsic. The spot-pinned BSM curve (what every theta-decay illustration actually plots) says it should have lost 31%. The real curve decays at roughly **double** the textbook rate, the whole way down.
**The ranking is inverted.**
Theory says a fixed OTM strike decays *faster* than ATM. In the data, the wings **outlive** the body: at 21 DTE the 25Δ strangle still holds 57% of its extrinsic while the ATM straddle holds 29%.
Why this happens (no mystery, no "edge" claim):
- The textbook curve assumes spot stays glued to your strike. It doesn't. Spot wanders — which *drains* extrinsic from the ATM strike it left behind and *feeds* extrinsic to whichever wing it approaches.
- It's a gamma/path effect, priced in and well understood — but it means the decay chart everyone reasons from describes a contract that stops existing the moment the market moves. If you buy an ATM option and the market trends, your extrinsic doesn't follow the hockey stick; it follows the yellow line.
What it's NOT saying: extrinsic disappearing is not seller P&L.
- A short straddle "collects" that extrinsic but pays out intrinsic when spot moves — this chart is about where time value goes, not about who profits.
**Limitations:**
- Calendar-day DTE → you can see a 7-day weekend sawtooth in the curves.
- Medians of normalized paths; means are noisier but same shape.
- Two data regimes (true EOD 2007–2014, last-hourly-snapshot 2015–2026) — I split the sample by era and the shape/ranking is identical in both halves.
- Extrinsic floored at 0 (deep-ITM mids occasionally print under intrinsic).
- SPY only. Single-name behavior (earnings, harder-to-borrow) will differ.
- Deep-ITM puts near ex-div carry early-exercise richness — second order at these strikes.
