Funding Rate

The funding rate is a mechanism exclusive to crypto perpetual pairs that periodically transfers payments between longs and shorts—longs pay shorts when the rate is positive, and shorts pay longs when it’s negative. It’s a zero-sum fee settled directly among traders, designed to incentivize traders to neutralize their delta exposure.

It’s determined by three components:

  1. Open-Interest Imbalance (a bigger imbalance leads to bigger funding rates)

  2. Theoretical Funding Rate (based on open-interest imbalance)

  3. Convergence Regime (how quickly the current rate moves toward the theoretical rate)


1. Open-Interest Imbalance

We normalize long/short open interest into a single variable xx:

x=OIlongāˆ’OIshortOIcaps ,x∈[āˆ’1,1] x = \frac{\mathrm{OI}_{\mathrm{long}} - \mathrm{OI}_{\mathrm{short}}}{\mathrm{OI}_{\mathrm{caps}}} \,,\qquad x \in [-1,1]

2. Theoretical Funding Rate

The Hill function maps imbalance xx to an equilibrium funding rate H(x)H(x):

H(x)={R1 (a x)n(a x)n+bā€…ā€Š+ā€…ā€ŠCx≄0,āˆ’ā€‰R2 (a x)n(a x)n+bā€…ā€Š+ā€…ā€ŠCx<0. H(x) = \begin{cases} R_{1}\,\displaystyle\frac{(a\,x)^{n}}{(a\,x)^{n} + b}\;+\;C & x \ge 0,\\[12pt] -\,R_{2}\,\displaystyle\frac{(a\,x)^{n}}{(a\,x)^{n} + b}\;+\;C & x < 0. \end{cases}
  • R1,R2R_{1}, R_{2}​: maximum upward/downward rate contributions

  • a,b,na, b, n: shape parameters controlling steepness and midpoint

  • CC: base funding offset


3. Convergence Dynamics

Holding xx constant ( dxdt=0\frac{dx}{dt}=0 ), the actual funding rate y(t)y(t) relaxes toward H(x)H(x) at a speed set by A(x)A(x):

dy(t)dtā€…ā€Š=ā€…ā€Šāˆ’ā€‰A(x) [y(t)āˆ’H(x)]. \frac{dy(t)}{dt} \;=\; -\,A(x)\,\bigl[y(t) - H(x)\bigr].
  • If y(t)>H(x)y(t)>H(x), the funding rate decays downward; if y(t)<H(x)y(t)<H(x), it rises upward.

  • A(x)A(x) varies by market regime:

    Regime
    Condition
    Speed

    Slow (Dumping)

    Imbalance is decreasing

    Slowest

    Default (Pulling)

    Imbalance is increasing

    Moderate

    Fast (Dumping + Pulling)

    Imbalance switches sign

    Fastest


With this structure, the funding rate always moves smoothly toward the imbalance-driven equilibrium, adapting speed based on how participants’ positions shift.

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