Avellaneda–Stoikov

crates/vike-mm/src/avellaneda.rs is the optional pricing layer SpreadMaker::with_avellaneda_stoikov turns on. It is "net-new Rust with NO Python twin (like SpreadMaker itself), so 'parity' means self-consistent reference-value pinning + neutral-reduction, not oracle bits." Its output is a (bid, ask) pair that "still flows UNCHANGED into the size-skew → breaker → filtration → modify-in-place tail" of quote emission, "so A-S inherits the adverse-selection guard it classically lacks."

The closed forms

The module header states them, "adapted to Polymarket's 0–1 bounded prices":

reservation price   r      = s − q_norm · γ · V
optimal half-spread δ_half = ½·γ·V + (1/γ)·ln(1 + γ/κ)
effective variance  V      = min(σ̂²·H, p·(1−p))

s is the fair mid, q_norm the size-normalised signed inventory, γ risk aversion, κ the fill-intensity decay, H the effective horizon (min(τ_hold, T−t) where a resolution time is known, τ_hold alone otherwise), and p = s the current probability. "The Bernoulli cap p(1−p) makes skew and spread vanish at the 0/1 walls (V→0) and peak at p=0.5 — the defensible adaptation that keeps A-S from over-penalising inventory near a wall." The half-spread is decomposed into as_vol_halfspread (½·γ·V) and as_intensity_halfspread ((1/γ)·ln(1+γ/κ)), "so the floor is a clean bit-anchor when V == 0".

Each input has one owner. AsState::fair_value takes the raw mid, or with use_micro_price the micro-price "weighted toward the side with LESS resting size"; a one-sided book returns None. q_norm = position / q_scale, with q_scale = 0 treated as 1. update_sigma2 is one EWMA step of the per-ms mid variance, inst = Δ²/Δt, with α = 1 − 0.5^(1/half_life). horizon_ms returns τ_hold under HorizonMode::ConstantTau, and min(τ_hold, T−t) under TimeToResolution once a resolution_ts is known — without one it returns τ_hold there too. bounded_variance implements the three VarianceModes — LocalCapped (the default), PureBernoulli, RawLocal — clamped at 0. κ comes from effective_kappa, the subject of intensity fits.

AsParams::default is "the recommended Polymarket starting configuration": gamma 0.1, tau_hold_ms 3 600 000, resolution_blackout_ms 60 000, a kappa_default of 50 — "used directly in KappaMode::Fixed", the default mode, and unclamped there — with kappa_min 1 and kappa_max 1000, which clamp a fitted κ in crates/vike-mm/src/fits.rs's fit_kappa, sigma_half_life 32, trade_window_ms 60 000, n_min 20, q_scale 100 and a one-tick min_standoff_ticks. horizon_mode defaults to TimeToResolution with resolution_ts unset, so on the recommended configuration that hour is the whole horizon until a profile names a resolution time.

The price domain

The 0–1 geometry "is now ONE case of a PriceDomain knob". domain_bounds resolves the posted walls: UnitInterval gives (tick, 1 − tick) "with the SAME arithmetic the layer hard-coded before the generalization"; Unbounded gives (−∞, +∞), for which the clamp "is an exact no-op"; Band { lo, hi } gives explicit walls. Two pairings "are load-bearing for a $-scale mount": VarianceMode::RawLocal, because "the Bernoulli cap goes negative for p > 1", and a min_half_spread_ticks floor, because "the adverse-selection half-spread is sub-tick at $-scale, so without it bid/ask snap to one tick."

The width ladder

bounded_half_spread is "THE WIDTH LADDER — the single authority on how a raw model half-spread becomes the posted one". Three stages, and "the ORDER is the whole design": the min_half_spread_ticks floor (the sub-tick guard); the max_half_spread_ticks cap, re-floored so "a max < min misconfig can never sacrifice the two-sided quote"; and the break-even fee_floor from break_even_half_spread, which is ½ · round_trip_fee_rate · s — "one leg's rate times the price, even though the bar being cleared is the whole round trip."

The third stage does not join the max(floor, cap) idiom. When fee_floor_exceeds_cap, "the answer is None: post nothing", because the cap answers "how wide may I go and still hope to fill?" and the fee floor "how wide must I be to not lose money?", and when they disagree "that is a fact about the INSTRUMENT … not about the tuning". The measurement behind the rule: "on prod2's bybit BTCUSDT mount: a 60-tick ceiling ⇒ ≤ 1.903 bp of capture against a 4.000 bp round-trip fee, i.e. −3.94 bp per round trip, forever."

Assembly

assemble_quote is "the affine two-sided posting geometry shared by A-S/GLFT and the Group-B model overrides": bid (r − d).min(s − standoff), ask (r + d).max(s + standoff) so "inventory skew can't push a quote across s", the wall clamp, a grid snap through snap_to_tick (which uses vike_model::round_to_step, round-half-to-even), and acceptance only of "a genuine, correctly-ordered two-sided quote that still straddles the fair mid" — lo ≤ bid < s < ask ≤ hi. Otherwise None, the same hold contract as a one-sided book.

Three resolution-aware terms live in this file too. Inside the blackout — in_blackout, only under TimeToResolution with a known resolution_ts and a positive window — price returns widest_quote, "stay two-sided but push fills out to the extreme walls"; effective_blackout_ms widens that window near the money by 1 + atm_blackout_scale·exp(−z²/2). terminal_var adds γ_term · w(τ) · p(1−p) into V over the last terminal_ramp_ms, because the settlement variance "does NOT vanish as τ → 0 — unlike the diffusion term". blended_anchor pulls the priced mid toward p_up(underlying) by underlying_weight; "only the pricing sees this — the σ̂²/κ estimators keep the raw book mid." The rest of the resolution machinery is on settlement.

GLFT through the same assembly

gueant_skew_coeff is the Guéant–Lehalle–Fernandez-Tapia stationary coefficient S = √(σ̂²·γ / (2·κ·A) · (1 + γ/κ)^(1 + κ/γ)), A the base fill intensity at the touch "per ms, matching the per-ms σ̂² — the units MUST agree". effective_variance feeds it to the shared assembly as V_eff = S/γ, "which makes the posted depths c1 + (½ ± q)·S — the SAME affine form A-S emits with γ·V"; the horizon, the settlement term and the Bernoulli cap "are all IGNORED here (GLFT is horizon-free)". The glft_equals_avellaneda_stoikov_at_matching_variance test pins the identity as bit-exact.

Two paths through price

With ReservationModel::AsLinear, SpreadSource::AsOptimal, both alpha weights, running_penalty_phi and force-flatten all off, AsState::price returns as_quotes — "the verbatim pre-Group-B call, so the fast path is byte-identical BY CONSTRUCTION". Anything else takes the override path: swap the reservation (the LMSR walk on binary outcomes), add the Cartea–Jaimungal shift (short-term alpha) and the force-flatten skew, swap the half-spread source, then run "the SAME width ladder as_quotes runs" and the same assemble_quote.