Implied Future & Discount From Option Quotes

This notebook computes the implied underlying future bid/ask from option quotes of a single expiry.

  • Computes an implied future quote \([F_{\text{bid}}, F_{\text{ask}}]\) and a discount range \([D_{\min}, D_{\max}]\) that are jointly consistent with the quoted calls & puts.

  • Identifies and excludes the fewest possible strikes whose quotes prevent any consistent solution (likely stale/misquoted lines).

  • Visualizes per-strike implied future intervals and the final \([F_{\text{bid}}, F_{\text{ask}}]\).

%matplotlib inline
import matplotlib.pyplot as plt
plt.rcParams["figure.dpi"] = 120

from volkit import estimate_future_from_option_quotes
from volkit.datasets import spxw

Read a set op example option quotes. Weekly S&P options with 7 days to expiry. Use only quotes that have been trades at least once (min_vol=1)

df = spxw(min_volume=1, D=7)

res, valid_mask = estimate_future_from_option_quotes(
   df['K'], 
   df['C_bid'], 
   df['C_ask'], 
   df['P_bid'], 
   df['P_ask'],
   plot=True
)

res
F2918.900000
F_bid2918.600000
F_ask2919.200000
D0.999083
D_min0.99066667
D_max1.00750000
../_images/c66391219bdd98e31969c2b6b8b1f293bb89d1dd1348f7687c776f39e6c42fa6.png

The plot

We plot, for each strike \(K_i\), a vertical bar from \(F_{\text{bid},i}\) to \(F_{\text{ask},i}\) (computed at a representative discount \(D^* = (D_{\min}+D_{\max})/2\):

  • Green bars: strikes that were kept (they all overlap with the final band).

  • Red bars: strikes that were excluded (their intervals don’t overlap the consensus). These are typically stale quotes (e.g., recorded when the underlying was briefly elsewhere) or fat-fingered lines, and they create arbitrage when combined with the rest of the book.

Two dashed black horizontal lines mark the final \(\big[F_{\text{bid}}, F_{\text{ask}}\big]\).
By construction, all green bars intersect this band.