Underlying & |Delta| Slice
Choose an underlying S and a |Δ| level at a reference DTE. We solve for the strike K
such that the option has that |Δ| at that maturity, then keep K fixed for all DTE in the chart.
“Reference DTE” is the maturity where you define your |Δ| slice (e.g. 30 days → “40Δ at 30DTE”).
We compute K at that DTE and then keep that same K when plotting θ or Δ vs DTE.
Market Inputs & Max DTE
Volatility, rate, dividend yield, and chart horizon.
X‑axis shows the option’s own DTE (days to expiration), from the chosen max DTE on the left
down to 0 on the right.
Probe DTE & Theta Stats
Probe line always within the chart: 0 ≤ probe DTE ≤ max DTE.
Call θ / day @ probe DTE
Put θ / day @ probe DTE
Call θ / day @ ATM (K = S)
Put θ / day @ ATM (K = S)
All values are per 1 underlying unit; short positions flip the sign.
Notes:
It may be observed that for some options, close to expiration, theta on long puts becomes positive. This is due to the different effect of interest rate on puts and calls. See https://quant.stackexchange.com/questions/68153/what-is-the-intuition-behind-a-positive-theta-for-european-long-puts.
Theta per Day vs Days‑to‑Expiration
|Δ| and reference DTE define a strike K (e.g. “40Δ at 30DTE”). We then hold that K fixed and plot how
θ or Δ evolves as the option’s own DTE moves from max DTE → 0.
Call
Put
Zero line