8idZddlZddlmZmZmZdedefdZddeededefd Z dd eed edefd Z dd ededededededefdZ dededee effdZ dedefdZy)u PolyEdge — Fair Value Model for Binary Options Prices a "Will BTC be above $X in T minutes?" binary option using: 1. Log-normal model (Black-Scholes-style) for base fair value 2. Realized volatility (EWMA) for vol estimate 3. Momentum adjustment for short-term drift 4. Mean-reversion overlay for extreme prices Fair Value = Φ((ln(S/K) + μT) / (σ√T)) Where: S = current BTC price K = strike price σ = annualized realized volatility μ = drift (momentum-adjusted) T = time to expiry in years Φ = standard normal CDF N)ListOptionalTuplexreturncd}d}d}d}d}d}d}|dkr d }t|}d d ||zzz }d ||z|z|z|z|z|z|z|z|ztj| |zd z zz } d d || zzzS) z:Approximate standard normal CDF using Abramowitz & Stegun.g~Z O?gi<15ҿgWU?g9LW@g-UB?g{=@?r?@?)absmathexp) ra1a2a3a4a5psigntys 7/var/www/html/crpytotradingbot/polymarket/fair_value.pynorm_cdfrs B B B B B A D1u F sQU{A 26B;!#r)Q.3q82=BTXXqbSTfWZlE[[[A #q. !!returns ewma_spanct|dkryd|dzz }|ddz}|ddD]}||dzzd|z |zz}d}tj||z}t|dS) a Calculate realized volatility using EWMA of squared returns. Returns annualized vol (assuming 5-min bars, 252 trading days). Args: returns: List of log returns ewma_span: EWMA span for smoothing Returns: Annualized volatility r r r rN頚g?)lenrsqrtmax)rralphaewma_varr bars_per_year annual_vols r realized_volr*,s 7|a 9q= !EqzQH QR[=AF#q5yH&<<= M8m34J z4  rpriceslookbackct||dzkry|| d}tj|d|dz }d}||z }||z}|S)z Estimate short-term drift from recent price momentum. Args: prices: Recent close prices lookback: Number of bars for momentum calc Returns: Annualized drift estimate r Nr rr!)r"rlog)r+r,recent total_returnr(per_bar_return annual_drifts rmomentum_driftr4Jsa 6{X\! XIJ F88F2J23LM!H,N!M1L r current_pricestrikevoltime_to_expiry_mindriftmomentum_weightc|dks |dks|dkry|dz }||z}|tj|z}|dkr ||kDrdSdStj||z |d|dzzz |zz|z } t| } t dt d | S) uK Calculate fair value of a binary option "BTC above strike at expiry". Uses log-normal model: FV = Φ((ln(S/K) + (μ - σ²/2)T) / (σ√T)) With momentum-adjusted drift: μ_adj = drift * momentum_weight Args: current_price: Current BTC price strike: Strike price of the binary vol: Annualized volatility time_to_expiry_min: Minutes until resolution drift: Annualized momentum drift momentum_weight: Weight for momentum (0 = ignore, 1 = full) Returns: Fair value between 0 and 1 rr i g|=r r.r g{Gz?gGz?)rr#r/rr$min) r5r6r7r8r9r:Tmu sigma_sqrt_td2 fair_values rcalc_fair_valuerBds8Vq[C1H m,A  B1%Le#f,s5#5 ((=6) *b3a<.?1-D D TB"J tSz* ++rrA market_pricecD||z }|dkDrd|fS|dkr dt|fSy)aP Calculate trading edge: difference between fair value and market price. Returns: (direction, edge_magnitude) direction: "buy_yes" if FV > market (YES is cheap) "buy_no" if FV < market (NO is cheap / YES is expensive) edge: absolute mispricing (always positive if tradeable) rbuy_yesbuy_no)noner.)r)rArCedges r calc_edgerIs8  $D ax$ T""rc8|dkDr|dz dzS|dkrd|z dzSy)a, Adjust edge for mean-reversion at extremes. When market price is very high (>0.85) or very low (<0.15), there's a statistical tendency to revert. This adds a small edge bonus for fading extreme prices. Returns: Additional edge (positive = fade the extreme) g333333?r g333333?r.)rCs rmean_reversion_adjustmentrLs7dt#s**  |#s** r)))g@r.g333333?)__doc__rtypingrrrfloatrintr*r4rBstrrIrLrKrrrTs& ((""%"(!$u+!#!u!<4;#e<!$ 1,1, 1, 1, 1,  1,  1, 1,h%usEz9J(Eer