Function hull_white_compounded_convexity_exponent 

pub fn hull_white_compounded_convexity_exponent<R: Scalar>(
    start: f64,
    end: f64,
    sigma: R,
    mean_reversion: R,
) -> R

The exponent Λ of the Hull–White futures convexity for an overnight rate compounded in arrears from start to end (years from today, start the first instant not yet fixed): under the model E[exp ∫ₛᴱ r] = P(0, s)/P(0, E) · e^Λ (Mercurio 2018), with

Λ = Λ_term(s, E) + σ² ∫₀^τ B(θ)² dθ
  = Λ_term(s, E) + σ²/a² · (τ − 2(1 − e^{−aτ})/a + (1 − e^{−2aτ})/(2a)),   τ = E − s

— Λ = Var ∫ₛᴱ x + Cov(∫₀ˢ x, ∫ₛᴱ x) for the model’s Gaussian factor x. The part of the variance and the covariance carried from before s are exactly the term contract’s exponent hull_white_convexity_exponent over [s, E]; what the term rate lacks is the variance accrued while the period fixes. For |aτ| < 0.5 the in-period part is summed as its series σ²τ³ Σ_{k≥3} (−1)^{k+1}(2^{k−1} − 2)(aτ)^{k−3}/k!, so it tends to the Ho–Lee σ²τ³/3 without cancellation. In the mode, so σ and a differentiate.