PythagorasGoal/scripts/research/r0724_pm_deribit_probe.py

"""r0724_pm_deribit_probe — Riconciliazione LIVE Polymarket <-> Deribit su digitali BTC/ETH.

Domanda: quanto del "gap ~11pp" (arXiv 2606.19517, PM vs prob implicite Deribit) sopravvive
OGGI a una riconciliazione onesta che aggiusta i mismatch di SPEC, e il trade hedged
(lato cheap su PM + digitale opposta via VERTICAL di opzioni Deribit) ha senso a ~$600?

Mismatch di spec quantificati (non assunti):
  1. TEMPO: i PM "above $K on <date>" risolvono sulla candela 1m Binance delle 12:00 ET
     (=16:00 UTC in estate); le daily Deribit scadono 08:00 UTC (settlement TWAP 30m
     dell'indice) -> 8h di varianza extra lato PM. dP_time = N(d2;T_pm) - N(d2;T_der).
  2. FONTE: PM risolve su Binance BTC/USDT; Deribit su indice BTC-USD. Basis misurato
     live (= sconto USDT/USD): pochi bps di spot MA a orizzonte daily con IV ~15%
     vale svariati pp di probabilita' ATM. dP_src = N(d2; S*(1+basis)) - N(d2; S).
  3. REPLICA: la digitale via vertical ha bound sub/super-replicanti:
     call-spread [K,K+w] <= 1{S>K} <= call-spread [K-w,K] (identico coi put OTM).
     Lato ITM i book Deribit sono MORTI -> si replica SEMPRE dal lato OTM
     (K>=S: call; K<S: put, P_above = 1 - put_spread/w). Stima centrale = spread
     centrato [K-w,K+w] sui mark; banda = [sub_mark, super_mark]; eseguibile =
     sub-replica incrociando bid/ask REALI.
  4. COSTI: PM fee 0 ma spread+depth CLOB; Deribit taker 0.0003 ccy/contratto cap
     12.5% del premio per gamba + delivery 0.00015 (cap 12.5%) sul leg ITM; margine
     del leg corto in standard margin (nessun netting del vertical in SM).
  5. RISCHIO NON HEDGIABILE: P(cross) = probabilita' che S stia da lati OPPOSTI di K
     alle 08:00 e alle 16:00 UTC (le due gambe risolvono in conflitto -> payoff 0 o 2):
     MC bivariato con sigma implicita. Vicino all'ATM e' grande -> il "lock" non esiste.

Tutto live, API pubbliche tokenless, zero storage; se un endpoint e' vuoto lo dichiara.
Riproducibile: uv run python scripts/research/r0724_pm_deribit_probe.py
"""
from __future__ import annotations

import json
import math
import random
import time
import urllib.request
from datetime import datetime, timezone

UA = {"User-Agent": "Mozilla/5.0 (research probe)"}


def get(url: str, timeout: int = 20, retries: int = 2):
    for k in range(retries + 1):
        try:
            req = urllib.request.Request(url, headers=UA)
            with urllib.request.urlopen(req, timeout=timeout) as r:
                return json.load(r)
        except Exception as e:  # noqa: BLE001
            if k == retries:
                print(f"  [FETCH FAIL] {url[:100]} -> {e}")
                return None
            time.sleep(1.0)


def ncdf(x: float) -> float:
    return 0.5 * (1.0 + math.erf(x / math.sqrt(2.0)))


def bs_digital(S: float, K: float, sig: float, T_yr: float) -> float:
    if T_yr <= 0 or sig <= 0:
        return 1.0 if S > K else 0.0
    d2 = (math.log(S / K) - 0.5 * sig * sig * T_yr) / (sig * math.sqrt(T_yr))
    return ncdf(d2)


# ----------------------------------------------------------------------------- Polymarket
PM_EVENTS = [
    ("BTC", "bitcoin-above-on-july-25-2026", "25JUL26"),
    ("ETH", "ethereum-above-on-july-25-2026", "25JUL26"),
    ("BTC", "bitcoin-above-on-july-26-2026", "26JUL26"),
    ("ETH", "ethereum-above-on-july-26-2026", "26JUL26"),
    ("BTC", "bitcoin-above-on-july-27-2026", "27JUL26"),
    ("ETH", "ethereum-above-on-july-27-2026", "27JUL26"),
]


def parse_strike(question: str) -> float | None:
    import re

    m = re.search(r"\$([\d,]+(?:\.\d+)?)", question)
    return float(m.group(1).replace(",", "")) if m else None


def fetch_pm():
    out = []
    for asset, slug, dexp in PM_EVENTS:
        ev = get(f"https://gamma-api.polymarket.com/events?slug={slug}")
        if not ev:
            print(f"[PM] evento {slug}: VUOTO/bloccato")
            continue
        ev = ev[0]
        for m in ev["markets"]:
            K = parse_strike(m["question"])
            if K is None:
                continue
            desc = m.get("description", "")
            tok = json.loads(m.get("clobTokenIds", "[]"))
            out.append(
                dict(
                    asset=asset,
                    dexp=dexp,
                    end=ev["endDate"],
                    K=K,
                    yes_bid=float(m["bestBid"]) if m.get("bestBid") else None,
                    yes_ask=float(m["bestAsk"]) if m.get("bestAsk") else None,
                    vol24=float(m.get("volume24hr") or 0),
                    spec_ok=("Binance" in desc and "12:00 in the ET" in desc),
                    yes_token=tok[0] if tok else None,
                )
            )
    return out


def pm_book_depth(token_id: str):
    b = get(f"https://clob.polymarket.com/book?token_id={token_id}")
    if not b or not b.get("bids") or not b.get("asks"):
        return None
    bids = [(float(x["price"]), float(x["size"])) for x in b["bids"]]
    asks = [(float(x["price"]), float(x["size"])) for x in b["asks"]]
    bb, ba = max(p for p, _ in bids), min(p for p, _ in asks)
    mid = 0.5 * (bb + ba)
    d = {}
    for w in (0.01, 0.02):
        d[w] = (
            sum(s * p for p, s in bids if p >= mid - w),
            sum(s * p for p, s in asks if p <= mid + w),
        )
    return dict(bb=bb, ba=ba, depth=d)


# ------------------------------------------------------------------------------- Deribit
def fetch_deribit(ccy: str):
    bs = get(
        "https://www.deribit.com/api/v2/public/get_book_summary_by_currency"
        f"?currency={ccy}&kind=option"
    )
    idx = get(
        f"https://www.deribit.com/api/v2/public/get_index_price?index_name={ccy.lower()}_usd"
    )
    ins = get(
        f"https://www.deribit.com/api/v2/public/get_instruments?currency={ccy}"
        "&kind=option&expired=false"
    )
    if not bs or not idx or not ins:
        return None
    books = {row["instrument_name"]: row for row in bs["result"]}
    expts = {}
    for i in ins["result"]:
        expts[i["instrument_name"].split("-")[1]] = i["expiration_timestamp"] / 1000.0
    return dict(books=books, index=idx["result"]["index_price"], expts=expts)


def _q(books, ccy, dexp, strike, typ, index):
    """(bid_usd, ask_usd, mark_usd) di uno strumento; None se assente."""
    n = f"{ccy}-{dexp}-{int(strike)}-{typ}"
    r = books.get(n)
    if not r:
        return None
    return dict(
        n=n,
        bid=(r["bid_price"] or 0.0) * index,
        ask=(r["ask_price"] * index) if r["ask_price"] else None,
        mark=(r.get("mark_price") or 0.0) * index,
    )


def deribit_digital(books, ccy, dexp, K, index):
    """Stima onesta di P(S_der > K) via vertical OTM-side.

    Ritorna: mark centrato, banda [sub_mark, super_mark], eseguibili
    (exec_buy = costo per COMPRARE la sub-replica dell'above-digitale ai prezzi reali;
     exec_sell = incasso per VENDERLA), gambe usate.
    """
    typ = "C" if K >= index else "P"
    strikes = sorted(
        float(n.split("-")[2])
        for n in books
        if n.split("-")[1] == dexp and n.endswith(f"-{typ}")
    )
    if K not in strikes:
        return None  # tutti gli strike PM qui coincidono con strike listati
    i = strikes.index(K)
    if i == 0 or i == len(strikes) - 1:
        return None
    Km, Kp = strikes[i - 1], strikes[i + 1]
    qm, q0, qp = (
        _q(books, ccy, dexp, Km, typ, index),
        _q(books, ccy, dexp, K, typ, index),
        _q(books, ccy, dexp, Kp, typ, index),
    )
    if not (qm and q0 and qp):
        return None

    if typ == "C":
        centered = (qm["mark"] - qp["mark"]) / (Kp - Km)
        sub = (q0["mark"] - qp["mark"]) / (Kp - K)  # <= P
        sup = (qm["mark"] - q0["mark"]) / (K - Km)  # >= P
        # comprare sub-replica: buy C(K), sell C(Kp)
        exec_buy = (
            (q0["ask"] - qp["bid"]) / (Kp - K) if q0["ask"] is not None else None
        )
        exec_sell = (
            (q0["bid"] - qp["ask"]) / (Kp - K) if qp["ask"] is not None else None
        )
        legs = (q0, qp)
    else:
        # P_above = 1 - put_spread/w ; [K,Kp] put spread super-replica il below
        centered = 1.0 - (qp["mark"] - qm["mark"]) / (Kp - Km)
        sub = 1.0 - (qp["mark"] - q0["mark"]) / (Kp - K)  # <= P_above
        sup = 1.0 - (q0["mark"] - qm["mark"]) / (K - Km)  # >= P_above
        # comprare (sinteticamente) l'above = VENDERE il put spread [K,Kp]:
        # incasso bid(Kp)-ask(K); prezzo implicito pagato = 1 - incasso/w
        exec_buy = (
             1.0 - (qp["bid"] - q0["ask"]) / (Kp - K) if q0["ask"] is not None else None
        )
        exec_sell = (
            1.0 - (qp["ask"] - q0["bid"]) / (Kp - K) if qp["ask"] is not None else None
        )
        legs = (q0, qp)
    return dict(
        typ=typ,
        Km=Km,
        Kp=Kp,
        w=Kp - K,
        centered=centered,
        sub=sub,
        sup=sup,
        exec_buy=exec_buy,
        exec_sell=exec_sell,
        legs=legs,
    )


IV_CACHE: dict = {}


def deribit_iv(ccy: str, dexp: str, name: str) -> float | None:
    if name in IV_CACHE:
        return IV_CACHE[name]
    t = get(f"https://www.deribit.com/api/v2/public/ticker?instrument_name={name}")
    iv = None
    if t:
        iv = t["result"].get("mark_iv")
        iv = iv / 100.0 if iv else None
    IV_CACHE[name] = iv
    return iv


def p_cross(S, K, sig, T1_yr, T2_yr, n=200_000, seed=7):
    """MC: P(lati opposti di K a T1 e T2) e P(sopra a T2 ma sotto a T1) ecc."""
    rng = random.Random(seed)
    lo_hi = hi_lo = 0
    lnK = math.log(K / S)
    s1 = sig * math.sqrt(T1_yr)
    s2x = sig * math.sqrt(max(T2_yr - T1_yr, 1e-12))
    for _ in range(n):
        x1 = -0.5 * s1 * s1 + s1 * rng.gauss(0, 1)
        x2 = x1 - 0.5 * s2x * s2x + s2x * rng.gauss(0, 1)
        a, b = x1 > lnK, x2 > lnK
        if not a and b:
            lo_hi += 1
        elif a and not b:
            hi_lo += 1
    return lo_hi / n, hi_lo / n


# ----------------------------------------------------------------------------------- run
def main():
    now = datetime.now(timezone.utc)
    print(f"=== PROBE PM<->DERIBIT  {now.isoformat(timespec='seconds')} ===\n")

    pm = fetch_pm()
    nbad = sum(1 for m in pm if not m["spec_ok"])
    print(f"[PM] {len(pm)} mercati above/below; spec Binance/12:00ET non confermata su {nbad}")

    der = {c: fetch_deribit(c) for c in ("BTC", "ETH")}
    for c, d in der.items():
        if d:
            print(f"[Deribit] {c} index={d['index']:.2f}")

    def binance_spot(sym):
        for host in ("https://api.binance.com", "https://data-api.binance.vision"):
            r = get(f"{host}/api/v3/ticker/price?symbol={sym}", timeout=10, retries=0)
            if r and "price" in r:
                return float(r["price"])
        return None

    binance = {"BTC": binance_spot("BTCUSDT"), "ETH": binance_spot("ETHUSDT")}
    kr = get("https://api.kraken.com/0/public/Ticker?pair=USDTZUSD", timeout=10, retries=1)
    usdtusd = None
    try:
        usdtusd = float(list(kr["result"].values())[0]["c"][0])
    except Exception:  # noqa: BLE001
        pass
    print(f"[Binance] BTCUSDT={binance['BTC']} ETHUSDT={binance['ETH']} | USDT/USD={usdtusd}")
    basis = {}
    for c in ("BTC", "ETH"):
        basis[c] = (binance[c] / der[c]["index"] - 1.0) if (der[c] and binance[c]) else 0.0
        print(f"  basis {c} BinanceUSDT vs indice Deribit: {basis[c]*1e4:+.1f} bps")

    rows = []
    for m in pm:
        c, d = m["asset"], der[m["asset"]]
        if not d or m["dexp"] not in d["expts"]:
            continue
        S = d["index"]
        dig = deribit_digital(d["books"], c, m["dexp"], m["K"], S)
        if dig is None:
            continue
        T_der = max(d["expts"][m["dexp"]] - now.timestamp(), 0) / (365.25 * 86400)
        t_pm = datetime.fromisoformat(m["end"].replace("Z", "+00:00")).timestamp()
        T_pm = max(t_pm - now.timestamp(), 0) / (365.25 * 86400)
        near = abs(math.log(m["K"] / S)) < 0.09
        sig = deribit_iv(c, m["dexp"], dig["legs"][0]["n"]) if near else None
        if sig is None:
            sig = 0.45
        dP_time = bs_digital(S, m["K"], sig, T_pm) - bs_digital(S, m["K"], sig, T_der)
        dP_src = bs_digital(S * (1 + basis[c]), m["K"], sig, T_pm) - bs_digital(
            S, m["K"], sig, T_pm
        )
        pm_mid = (
            0.5 * (m["yes_bid"] + m["yes_ask"])
            if (m["yes_bid"] is not None and m["yes_ask"] is not None)
            else (m["yes_ask"] or m["yes_bid"])
        )
        raw = pm_mid - dig["centered"] if pm_mid is not None else None
        resid = raw - dP_time - dP_src if raw is not None else None
        depth = pm_book_depth(m["yes_token"]) if (m["yes_token"] and near) else None
        rows.append(
            dict(
                m=m,
                dig=dig,
                sig=sig,
                T_der=T_der,
                T_pm=T_pm,
                dP_time=dP_time,
                dP_src=dP_src,
                pm_mid=pm_mid,
                raw=raw,
                resid=resid,
                depth=depth,
                S=S,
                near=near,
            )
        )

    print("\n=== RICONCILIAZIONE (prob %, gap pp; digitale = vertical OTM-side) ===")
    hdr = (
        f"{'mkt':<22}{'PM b/a':>12}{'Der mark[sub,sup]':>20}{'exec b/s':>13}"
        f"{'raw':>7}{'dT':>6}{'dSrc':>6}{'resid':>7}{'iv%':>5}"
    )
    print(hdr)
    print("-" * len(hdr))
    for r in rows:
        m, g = r["m"], r["dig"]
        name = f"{m['asset']} >{int(m['K'])} {m['dexp'][:5]}"
        pmba = (
            f"{(m['yes_bid'] or 0)*100:.1f}/{(m['yes_ask'] or 0)*100:.1f}"
            if (m["yes_bid"] is not None or m["yes_ask"] is not None)
            else "n/a"
        )
        ex = (
            f"{g['exec_buy']*100:.0f}/{g['exec_sell']*100:.0f}"
            if (g["exec_buy"] is not None and g["exec_sell"] is not None)
            else "n/q"
        )
        print(
            f"{name:<22}{pmba:>12}"
            f"{g['centered']*100:>8.1f}[{g['sub']*100:.0f},{g['sup']*100:.0f}]".ljust(42)
            + f"{ex:>13}"
            f"{(r['raw'] or 0)*100:>+7.1f}{r['dP_time']*100:>+6.1f}"
            f"{r['dP_src']*100:>+6.1f}{(r['resid'] or 0)*100:>+7.1f}"
            f"{r['sig']*100:>5.0f}"
        )
    print(
        "\n  Der mark = spread centrato sui mark, [sub,sup] = bound di replica;"
        " exec b/s = comprare/vendere la sub-replica ai bid/ask REALI."
        "\n  raw = PM_mid - Der_mark; resid = raw - dT - dSrc"
        " (>0: PM sovraprezza il lato above vs Deribit spec-adjusted)."
    )

    # sistematicita' per bucket di moneyness
    print("\n=== RESIDUO PER BUCKET (solo quote PM a doppio lato) ===")
    buckets = {"ITM(K<S-1.5%)": [], "ATM(|1.5%|)": [], "OTM(K>S+1.5%)": []}
    for r in rows:
        if r["resid"] is None or r["m"]["yes_bid"] is None or r["m"]["yes_ask"] is None:
            continue
        lm = math.log(r["m"]["K"] / r["S"])
        b = "ITM(K<S-1.5%)" if lm < -0.015 else ("OTM(K>S+1.5%)" if lm > 0.015 else "ATM(|1.5%|)")
        buckets[b].append(r["resid"])
    for b, v in buckets.items():
        if v:
            pos = sum(1 for x in v if x > 0)
            print(
                f"  {b:<15} n={len(v):>2}  resid medio {sum(v)/len(v)*100:+.1f}pp"
                f"  mediana {sorted(v)[len(v)//2]*100:+.1f}pp  >0: {pos}/{len(v)}"
            )

    print("\n=== DEPTH CLOB PM (vicino allo spot) ===")
    for r in rows:
        if r["depth"]:
            m, dp = r["m"], r["depth"]
            d1, d2 = dp["depth"][0.01], dp["depth"][0.02]
            print(
                f"  {m['asset']} >{int(m['K'])} {m['dexp']}: book {dp['bb']:.3f}/{dp['ba']:.3f}"
                f"  depth±1c ${d1[0]:,.0f}/${d1[1]:,.0f}  ±2c ${d2[0]:,.0f}/${d2[1]:,.0f}"
                f"  vol24h ${m['vol24']:,.0f}"
            )

    # ------------------------------------------------------------------ trade hedged demo
    print("\n=== TRADE HEDGED a size minima (0.1 BTC / 1 ETH) — numeri VERI ===")
    min_amt = {"BTC": 0.1, "ETH": 1.0}
    fee_rate, dlv_rate = 0.0003, 0.00015
    for r in rows:
        m, g = r["m"], r["dig"]
        if r["resid"] is None or not r["near"] or abs(r["resid"]) < 0.01:
            continue
        if g["exec_buy"] is None or g["exec_sell"] is None:
            continue
        c, S = m["asset"], r["S"]
        amt = min_amt[c]
        W = g["w"] * amt  # notional digitale $
        if r["resid"] > 0:
            # PM ricco sul lato above: buy PM NO al (1-yes_bid) + buy digitale-above Deribit
            pm_px = 1 - (m["yes_bid"] or 0)
            der_px = g["exec_buy"]
            side = "BUY PM NO + LONG vertical OTM (sub-replica above)"
        else:
            pm_px = m["yes_ask"] or 1
            der_px = 1 - g["exec_sell"]
            side = "BUY PM YES + SHORT vertical OTM (sub-replica below)"
        cost = (pm_px + der_px) * W
        lock = W - cost
        fees = 0.0
        for leg in g["legs"]:
            fees += min(fee_rate * amt * S, 0.125 * leg["mark"] * amt)
        dlv = min(dlv_rate * amt * S, 0.125 * max(le["mark"] for le in g["legs"]) * amt)
        otm_frac = abs(g["Kp"] - S) / S
        mark_short = g["legs"][1]["mark"] / S
        im = (max(0.15 - otm_frac, 0.10) + mark_short) * amt
        pc = p_cross(S, m["K"], r["sig"], r["T_der"], r["T_pm"])
        capital = cost + im * S
        net = lock - fees - dlv
        days = r["T_pm"] * 365.25
        print(f"\n  {m['asset']} >{int(m['K'])} {m['dexp']}  resid {r['resid']*100:+.1f}pp -> {side}")
        print(
            f"    gambe Deribit {g['legs'][0]['n']}/{g['legs'][1]['n']} amount {amt} {c}"
            f" -> payout digitale ${W:,.0f}"
        )
        print(
            f"    costo PM ${pm_px*W:,.2f} + Deribit ${der_px*W:,.2f} = ${cost:,.2f};"
            f" lock lordo ${lock:,.2f}; fee entry ${fees:.2f} + delivery ${dlv:.2f}"
            f" -> netto ${net:,.2f}"
        )
        print(
            f"    margine leg corto (SM, no netting) ~${im*S:,.0f};"
            f" capitale impegnato ~${capital:,.0f};"
            f" ritorno se lock regge: {net/capital*100:.2f}% in {days:.1f}g"
            f" (~{net/capital*365.25/days*100:.0f}%/anno)"
        )
        print(
            f"    RISCHIO CROSS 08->16 UTC (MC, iv {r['sig']*100:.0f}%):"
            f" P(sotto@08,sopra@16)={pc[0]*100:.1f}%  P(sopra@08,sotto@16)={pc[1]*100:.1f}%"
            f"  -> P(gambe in conflitto)={sum(pc)*100:.1f}%"
        )

    print("\n[NOTE] Deribit settle = TWAP 30m pre-08:00 UTC vs PM candela 1m 16:00 UTC;")
    print("la sub-replica paga <1 nella rampa [K,K+w] -> il 'lock' e' un bound inferiore")
    print("solo FUORI dalla rampa; ATM con w=500 (BTC) la rampa e' ~1-1.5 sigma daily.")


if __name__ == "__main__":
    main()