Rho

What rho measures

In the classic model, a higher interest rate makes the strike, paid in the future, worth less today, which helps calls and hurts puts. Rho measures that effect per one percentage point of rate: a call rho of $38.7 means the call gains about $38.70 if rates rise from, say, 4% to 5%.

For the $100,000 BTC call with 30 days left and 50% implied volatility, rho is about +$38.7 against a price of $5,714; the matching put's rho is about −$43.4. A full point of rates moves the option by under 1%. With 7 days left, the call's rho is about $9.

Rho grows with time to expiry and with how deep in the money the option is. For long-dated options it starts to matter; for the weekly and monthly options where most crypto volume trades, it is small next to delta, vega and theta.

Where rates really show up in crypto

There is no single risk-free rate for bitcoin. What the options market does see is the forward price for each expiry, set by the futures market: a future usually trades above spot, and that premium (the basis) is the market's carry for holding BTC until then. It moves with funding conditions and demand for leverage, and it can be several percent a year above or below dollar rates.

Option venues price options against that forward. A change in "rates" therefore mostly reaches a crypto option through the forward: a richer basis raises the forward, which raises calls and lowers puts, the same way a delta move would. The +$38.7 above is the classic spot-model rho, which assumes the forward moves with the rate. Hold the forward fixed instead and a higher rate only discounts the payoff more: the call's rho would then be about −time × price / 100 ≈ −$4.70, small and negative.

You can read the market's own rate in two places on BOSS: the forward and basis per expiry on the Dashboard, and the implied rate of a box spread, whose payoff is set by its strikes alone. On coin-settled venues that payoff is the strike width divided by the settlement price, in coins, so the box prices a dollar rate only once converted; the box spread article explains how BOSS handles that.

How BOSS computes it

The structure's live rho on a strategy page comes from the venue's own Greeks, and only Deribit reports one: OKX and Bybit publish no rho, so there the live figure is 0 and only the curve is meaningful. The rho curve is computed with Black-Scholes at a zero rate, holding each leg's implied volatility fixed; it shows the shape of the sensitivity (larger in the money, larger for longer expiries) rather than a forecast of what a rate change would do.