How vol ratio is calculated

vol ratio = fee-implied volatility ÷ bid implied volatility of the gamma-matched option

Both sides are volatilities, so the ratio says how richly each market pays for the same price risk.

#1. Fee-implied volatility

Fee-implied volatility, written σ*, is the volatility a range's fees exactly pay for. Above it the range loses money, below it the range makes money.

For a $10,000 range of width ±w kept centred on the price:

1. Fees. Take the last seven days of fees the range would have earned, re-centred on the price as it moved and sharing each minute's fees with the liquidity actually in range at that minute. Minutes out of range earn nothing.
2. Costs that grow with volatility. Two costs rise with volatility σ:
   • LVR, the loss to arbitrage, grows with σ² and is larger for narrower ranges.
   • Re-centring: the price leaves the range more often as σ rises, and each re-centre costs a swap fee and price impact.
3. Solve for σ. σ* is the volatility at which fees equal LVR plus re-centring costs.

The formulas are in LVR and re-centring costs.

Seven days rather than one keeps a single busy afternoon from deciding the rating.

#2. The gamma-matched option

A range kept on the price has the same kind of risk as a short at-the-money option, but how much depends on its width. A tight range behaves like a very short-dated option; a wide one like a longer-dated option.

For each width, rangebound finds the option tenor with the same gamma per dollar as the range. For example, on a stock with 30% volatility, a ±5% range matches an option of about six days, a ±10% range one of about three weeks, and a ±25% range one of about four months.

rangebound then reads the bid implied volatility of the at-the-money option on the listed underlying at that tenor, interpolating between listed expiries up to about two months out. It uses the bid because an option writer receives the bid, not the mid.

Option chains are snapshotted every 30 minutes while the US market is open.

#3. The ratio, and which width is shown

The ratio is computed at every standard width from ±0.5% to ±50%. The headline is the widest width whose matching option is actually listed.

Why not show the best width? Fee-implied volatility barely changes with width, while option IV changes a lot along the term structure. Across widths, the ratio mostly traces the option market's term structure, so the maximum would simply pick whichever expiry is cheapest. The widest listed width is the most comparable, fully quoted benchmark.

When no width's matching option is listed, the widest width is used with the nearest expiry, and the ratio is marked ≈. The full picture across widths is in the pool page's Vol ratio by width tab.

#Vol spread

The Width vs net edge table also shows the vol spread, the same comparison as a difference:

vol spread = σ* − bid IV        in volatility points

A spread of +8 points and a ratio of 1.4× say the same thing in two ways.

#Assumptions

• Prices move continuously: no jumps. Real opening gaps cost a range more than LVR assumes.
• Re-centring is instant, and swaps to re-centre go through the same pool.
• The pool's volume doesn't depend on your position.
• The listed underlying's option IV is the right benchmark for its token. Tokens trade 24/7 and options don't, so overnight moves in the token aren't priced by the options.