feat: backtest

backend/routers/backtest.py

@@ -3,22 +3,52 @@ from pydantic import BaseModel
 from typing import Optional, List
 import yfinance as yf
 import numpy as np
-import pandas as pd
-from datetime import datetime
 from services.options_pricer import black_scholes
+from services.backtest_strategies import STRATEGIES, build_legs, synthetic_expiry
 
 router = APIRouter(prefix="/api/backtest", tags=["backtest"])
 
 
+@router.get("/symbols")
+def backtest_symbols():
+    """Underlyings actually tracked via Saxo (Config → Instruments Watchlist, linked to a
+    real Saxo options chain) — same yfinance-compatible `ticker` field used everywhere
+    else in the app, so pricing here still runs off yfinance's long history, but the
+    choices on screen match what's genuinely tradeable rather than an arbitrary ETF list."""
+    from services.database import get_instruments_watchlist
+    return [
+        {"ticker": w["ticker"], "name": w["name"]}
+        for w in get_instruments_watchlist() if w.get("saxo_option_symbol")
+    ]
+
+
+@router.get("/strategies")
+def backtest_strategies():
+    return [{"key": k, "label": label, "n_legs": n} for k, label, n in STRATEGIES]
+
+
 class BacktestRequest(BaseModel):
     symbol: str
     start_date: str
     end_date: str
-    strategy: str  # "long_call" | "long_put" | "bull_call_spread" | "bear_put_spread" | "straddle"
+    strategy: str
-    strike_offset_pct: float = 0.05  # e.g. 5% OTM
+    strike_offset_pct: float = 0.05  # e.g. 5% OTM — used by the 6 direct (non-template) strategies
     expiry_days: int = 90
     capital: float = 1000.0
-    geo_filter: Optional[str] = None  # optional pattern id to filter
+
+
+def _settle_leg(leg: dict, near_days: int, S_settle: float, sigma: float, r: float) -> float:
+    """Value one leg at the near expiry: intrinsic if it expires there too (the common
+    case), else a fresh Black-Scholes price for its remaining time (calendar/diagonal's
+    far leg — closed alongside the near leg rather than held to its own later expiry,
+    the standard way these are actually managed)."""
+    remaining_days = leg["days_to_expiry"] - near_days
+    if remaining_days <= 0:
+        if leg["option_type"] == "call":
+            return max(0.0, S_settle - leg["strike"])
+        return max(0.0, leg["strike"] - S_settle)
+    T = remaining_days / 365
+    return float(black_scholes(S_settle, leg["strike"], T, r, sigma, leg["option_type"])["price"])
 
 
 @router.post("/run")
@@ -32,11 +62,12 @@ def run_backtest(req: BacktestRequest):
         hist = hist.reset_index()
         returns = np.log(hist["Close"] / hist["Close"].shift(1)).dropna()
 
+        far_days = req.expiry_days * 2  # calendar/diagonal's far leg, closed alongside the near leg
+
         trades = []
         equity = [req.capital]
         capital = req.capital
         r = 0.05
-        T_open = req.expiry_days / 365
 
         step = max(1, req.expiry_days // 3)
         for i in range(0, len(hist) - req.expiry_days, step):
@@ -51,26 +82,33 @@ def run_backtest(req: BacktestRequest):
             if sigma < 0.01:
                 sigma = 0.20
 
-            if req.strategy in ["long_call", "bull_call_spread"]:
+            near_expiry = synthetic_expiry(date_str, req.expiry_days, S)
-                K = S * (1 + req.strike_offset_pct)
+            far_expiry = synthetic_expiry(date_str, far_days, S) if req.strategy in ("calendar_spread", "diagonal_spread") else None
-            else:
+            legs = build_legs(req.strategy, S, req.strike_offset_pct, near_expiry, far_expiry)
-                K = S * (1 - req.strike_offset_pct)
+            if not legs:
+                continue
 
-            result = black_scholes(S, K, T_open, r, sigma, "call" if "call" in req.strategy else "put")
+            entry_premiums = []
-            premium = result["price"]
+            for leg in legs:
-            contracts = max(1, int((capital * 0.1) / (premium * 100)))
+                T = leg["days_to_expiry"] / 365
-            cost = contracts * premium * 100
+                premium = float(black_scholes(S, leg["strike"], T, r, sigma, leg["option_type"])["price"])
+                entry_premiums.append(premium)
+
+            signed_qty = [(1 if leg["position"] == "long" else -1) * leg["quantity"] for leg in legs]
+            net_premium = sum(sq * p for sq, p in zip(signed_qty, entry_premiums))  # >0 debit, <0 credit
+
+            risk_basis = max(abs(net_premium), 0.05 * S)
+            contracts = max(1, int((capital * 0.1) / (risk_basis * 100)))
+            cost = net_premium * contracts * 100
 
             expiry_idx = min(i + req.expiry_days, len(hist) - 1)
             S_expiry = float(hist.iloc[expiry_idx]["Close"])
             date_expiry = str(hist.iloc[expiry_idx]["Date"])[:10]
 
-            if req.strategy in ["long_call", "bull_call_spread"]:
+            exit_values = [_settle_leg(leg, req.expiry_days, S_expiry, sigma, r) for leg in legs]
-                intrinsic = max(0, S_expiry - K)
+            exit_signed_value = sum(sq * v for sq, v in zip(signed_qty, exit_values))
-            else:
-                intrinsic = max(0, K - S_expiry)
 
-            pnl = (intrinsic - premium) * contracts * 100
+            pnl = (exit_signed_value - net_premium) * contracts * 100
             capital += pnl
             equity.append(round(capital, 2))
 
@@ -79,12 +117,16 @@ def run_backtest(req: BacktestRequest):
                 "exit_date": date_expiry,
                 "strategy": req.strategy,
                 "S_entry": round(S, 2),
-                "K": round(K, 2),
+                "S_expiry": round(S_expiry, 2),
-                "premium": round(premium, 4),
+                "legs": [
+                    {"strike": round(leg["strike"], 2), "option_type": leg["option_type"],
+                     "position": leg["position"], "quantity": leg["quantity"],
+                     "days_to_expiry": leg["days_to_expiry"]}
+                    for leg in legs
+                ],
+                "net_premium": round(net_premium, 4),
                 "contracts": contracts,
                 "cost": round(cost, 2),
-                "S_expiry": round(S_expiry, 2),
-                "intrinsic": round(intrinsic, 4),
                 "pnl": round(pnl, 2),
                 "capital": round(capital, 2),
             })

backend/services/backtest_strategies.py

@@ -0,0 +1,147 @@
+"""
+Multi-leg strategy catalog for the Backtest page.
+
+Backtest simulates years of history (2022-2024 etc.) via a single trailing-realized-vol
+Black-Scholes price per leg (see routers/backtest.py) — there's no real option chain to
+draw strikes from that far back (accumulated Saxo history only covers the last few weeks,
+see services/option_chain.py's own docstring). The 14 template-based strategies below
+therefore reuse services.strategy_templates's offset-based generators (built for Strategy
+Builder against a REAL chain) against a SYNTHETIC strike grid centered on spot instead —
+same leg-selection logic, just fed a fabricated but structurally identical "expiry" dict.
+
+The 6 single/vertical strategies use `strike_offset_pct` directly (S * (1 +/- pct)),
+matching the original single-leg backtest's behavior exactly rather than going through
+the grid, since they don't need a strike LIST to pick from.
+
+Vertical spreads (bull/bear call/put) aren't in strategy_templates.py — Strategy Builder's
+own residual search finds them without needing a template — so they're defined locally
+here rather than added to that shared module, to avoid changing Strategy Builder's and
+Portfolio's already-shipped optimizer behavior as a side effect of this feature.
+"""
+from typing import Any, Dict, List, Optional, Tuple
+
+from services import strategy_templates as tmpl
+
+Leg = Dict[str, Any]
+
+# STRATEGIES entries are (key, label, n_legs) — n_legs is purely informational (frontend
+# leg-count badge), the actual leg count comes from what build_legs() returns.
+STRATEGIES: List[Tuple[str, str, int]] = [
+    ("long_call", "Long Call", 1),
+    ("long_put", "Long Put", 1),
+    ("bull_call_spread", "Bull Call Spread", 2),
+    ("bear_put_spread", "Bear Put Spread", 2),
+    ("bear_call_spread", "Bear Call Spread", 2),
+    ("bull_put_spread", "Bull Put Spread", 2),
+    ("long_straddle", "Long Straddle", 2),
+    ("short_straddle", "Short Straddle", 2),
+    ("long_strangle", "Long Strangle", 2),
+    ("short_strangle", "Short Strangle", 2),
+    ("call_ratio_spread", "Call Ratio Spread", 2),
+    ("put_ratio_spread", "Put Ratio Spread", 2),
+    ("calendar_spread", "Calendar Spread", 2),
+    ("diagonal_spread", "Diagonal Spread", 2),
+    ("call_butterfly", "Call Butterfly", 3),
+    ("put_butterfly", "Put Butterfly", 3),
+    ("call_condor", "Call Condor", 4),
+    ("put_condor", "Put Condor", 4),
+    ("iron_condor", "Iron Condor", 4),
+    ("iron_butterfly", "Iron Butterfly", 4),
+]
+
+_TEMPLATE_STRATEGY_KEYS = {s[0] for s in STRATEGIES[6:]}  # everything past the 6 direct ones
+
+_GRID_STEP_PCT = 0.02
+_GRID_HALF_WIDTH = 25  # strikes from -50% to +50% of spot in 2% steps — enough room for
+                        # strategy_templates' OFFSETS/WIDTHS (max reach ~10 steps either side)
+
+
+def synthetic_expiry(expiry_date: str, days_to_expiry: int, spot: float) -> Dict[str, Any]:
+    """A fabricated 'expiry' shaped exactly like services.option_chain.get_chain_slice's
+    real output (expiry_date/days_to_expiry/calls/puts with {strike} rows) — strategy_templates'
+    generators only ever read strike lists off it, so they work unmodified against this."""
+    strikes = [round(spot * (1 + i * _GRID_STEP_PCT), 4) for i in range(-_GRID_HALF_WIDTH, _GRID_HALF_WIDTH + 1)]
+    return {
+        "expiry_date": expiry_date, "days_to_expiry": days_to_expiry,
+        "calls": [{"strike": k} for k in strikes], "puts": [{"strike": k} for k in strikes],
+    }
+
+
+def _atm_index(strikes: List[float], spot: float) -> int:
+    return min(range(len(strikes)), key=lambda i: abs(strikes[i] - spot))
+
+
+def _at(strikes: List[float], idx: int) -> Optional[float]:
+    return strikes[idx] if 0 <= idx < len(strikes) else None
+
+
+def _leg(expiry: Dict[str, Any], strike: float, option_type: str, position: str, quantity: int = 1) -> Leg:
+    return {
+        "expiry_date": expiry["expiry_date"], "days_to_expiry": expiry["days_to_expiry"],
+        "strike": strike, "option_type": option_type, "position": position, "quantity": quantity,
+    }
+
+
+def _first_by_name(candidates: List[Tuple[str, List[Leg]]], name: str) -> Optional[List[Leg]]:
+    return next((legs for n, legs in candidates if n == name), None)
+
+
+def _vertical(expiry: Dict[str, Any], spot: float, offset_pct: float, option_type: str, buy_near: bool) -> List[Leg]:
+    """2-leg vertical, same expiry/type: one leg at spot*(1+/-offset_pct), the other at
+    3x that offset. buy_near=True -> debit spread (long the closer strike, short the
+    farther); False -> credit spread (short the closer, long the farther)."""
+    sign = 1 if option_type == "call" else -1
+    near_k = round(spot * (1 + sign * offset_pct), 4)
+    far_k = round(spot * (1 + sign * offset_pct * 3), 4)
+    near_pos, far_pos = ("long", "short") if buy_near else ("short", "long")
+    return [_leg(expiry, near_k, option_type, near_pos), _leg(expiry, far_k, option_type, far_pos)]
+
+
+def build_legs(
+    strategy_key: str, spot: float, strike_offset_pct: float,
+    near_expiry: Dict[str, Any], far_expiry: Optional[Dict[str, Any]],
+) -> List[Leg]:
+    """Returns the leg list for one of STRATEGIES' keys, or [] if it can't be built
+    (calendar/diagonal with no far_expiry, or the synthetic grid came up short)."""
+    if strategy_key == "long_call":
+        return [_leg(near_expiry, round(spot * (1 + strike_offset_pct), 4), "call", "long")]
+    if strategy_key == "long_put":
+        return [_leg(near_expiry, round(spot * (1 - strike_offset_pct), 4), "put", "long")]
+    if strategy_key == "bull_call_spread":
+        return _vertical(near_expiry, spot, strike_offset_pct, "call", buy_near=True)
+    if strategy_key == "bear_put_spread":
+        return _vertical(near_expiry, spot, strike_offset_pct, "put", buy_near=True)
+    if strategy_key == "bear_call_spread":
+        return _vertical(near_expiry, spot, strike_offset_pct, "call", buy_near=False)
+    if strategy_key == "bull_put_spread":
+        return _vertical(near_expiry, spot, strike_offset_pct, "put", buy_near=False)
+
+    if strategy_key not in _TEMPLATE_STRATEGY_KEYS:
+        return []
+
+    if strategy_key in ("long_straddle", "short_straddle", "long_strangle", "short_strangle"):
+        name = {"long_straddle": "Long Straddle", "short_straddle": "Short Straddle",
+                "long_strangle": "Long Strangle", "short_strangle": "Short Strangle"}[strategy_key]
+        return _first_by_name(list(tmpl.straddle_strangle(near_expiry, spot)), name) or []
+    if strategy_key in ("call_butterfly", "put_butterfly"):
+        name = "Call Butterfly" if strategy_key == "call_butterfly" else "Put Butterfly"
+        return _first_by_name(list(tmpl.butterfly(near_expiry, spot)), name) or []
+    if strategy_key == "iron_butterfly":
+        return _first_by_name(list(tmpl.iron_butterfly(near_expiry, spot)), "Iron Butterfly") or []
+    if strategy_key in ("call_condor", "put_condor"):
+        name = "Call Condor" if strategy_key == "call_condor" else "Put Condor"
+        return _first_by_name(list(tmpl.condor(near_expiry, spot)), name) or []
+    if strategy_key == "iron_condor":
+        return _first_by_name(list(tmpl.iron_condor(near_expiry, spot)), "Iron Condor") or []
+    if strategy_key in ("call_ratio_spread", "put_ratio_spread"):
+        name = "Call Ratio Spread" if strategy_key == "call_ratio_spread" else "Put Ratio Spread"
+        return _first_by_name(list(tmpl.ratio_spread(near_expiry, spot)), name) or []
+    if strategy_key == "calendar_spread":
+        if far_expiry is None:
+            return []
+        return _first_by_name(list(tmpl.calendar_spread(near_expiry, far_expiry, spot)), "Calendar Spread") or []
+    if strategy_key == "diagonal_spread":
+        if far_expiry is None:
+            return []
+        return _first_by_name(list(tmpl.diagonal_spread(near_expiry, far_expiry, spot)), "Diagonal Spread") or []
+    return []

frontend/src/hooks/useApi.ts

@@ -257,6 +257,22 @@ export const useBacktest = () =>
     mutationFn: (data) => api.post('/backtest/run', data).then(r => r.data),
   })
 
+export type BacktestSymbol = { ticker: string; name: string }
+export const useBacktestSymbols = () =>
+  useQuery<BacktestSymbol[]>({
+    queryKey: ['backtest-symbols'],
+    queryFn: () => api.get('/backtest/symbols').then(r => r.data),
+    staleTime: 60_000,
+  })
+
+export type BacktestStrategyInfo = { key: string; label: string; n_legs: number }
+export const useBacktestStrategies = () =>
+  useQuery<BacktestStrategyInfo[]>({
+    queryKey: ['backtest-strategies'],
+    queryFn: () => api.get('/backtest/strategies').then(r => r.data),
+    staleTime: 60 * 60_000,
+  })
+
 // ── AI ────────────────────────────────────────────────────────────────────────
 export const useAiStatus = () =>
   useQuery({

frontend/src/pages/Backtest.tsx

@@ -1,5 +1,5 @@
-import { useState } from 'react'
+import { useEffect, useState } from 'react'
-import { useBacktest } from '../hooks/useApi'
+import { useBacktest, useBacktestSymbols, useBacktestStrategies } from '../hooks/useApi'
 import clsx from 'clsx'
 import {
   AreaChart, Area, XAxis, YAxis, Tooltip, ResponsiveContainer,
@@ -8,17 +8,14 @@ import {
 import { History, Play, TrendingUp, TrendingDown, AlertTriangle } from 'lucide-react'
 import type { BacktestResult } from '../types'
 
-const STRATEGIES = [
+type LegRow = { strike: number; option_type: string; position: string; quantity: number; days_to_expiry: number }
-  { key: 'long_call', label: 'Long Call' },
-  { key: 'long_put', label: 'Long Put' },
-  { key: 'bull_call_spread', label: 'Bull Call Spread' },
-  { key: 'bear_put_spread', label: 'Bear Put Spread' },
-]
 
-const SYMBOLS = [
+function legsSummary(legs: LegRow[] | undefined): string {
-  'GLD', 'USO', 'WEAT', 'UNG', 'SPY', 'QQQ', 'GDX', 'COPX',
+  if (!legs || !legs.length) return '—'
-  'XLE', 'FXE', 'XOM', 'LMT', 'BA', 'RTX',
+  return legs
-]
+    .map(l => `${l.position === 'long' ? '+' : '−'}${l.quantity > 1 ? l.quantity + 'x' : ''}${l.option_type === 'call' ? 'C' : 'P'}${l.strike}`)
+    .join(' / ')
+}
 
 function StatCard({ label, value, sub, positive }: { label: string; value: string; sub?: string; positive?: boolean }) {
   return (
@@ -39,8 +36,11 @@ function StatCard({ label, value, sub, positive }: { label: string; value: strin
 export default function Backtest() {
   const { mutate: runBacktest, data: result, isPending } = useBacktest()
 
+  const { data: symbols } = useBacktestSymbols()
+  const { data: strategies } = useBacktestStrategies()
+
   const [form, setForm] = useState({
-    symbol: 'GLD',
+    symbol: '',
     start_date: '2022-01-01',
     end_date: '2024-12-31',
     strategy: 'long_call',
@@ -49,6 +49,12 @@ export default function Backtest() {
     capital: 1000,
   })
 
+  // Symbols only exist once Config → Instruments Watchlist has a Saxo-linked entry —
+  // default to the first one once it loads rather than a ticker that may not be there.
+  useEffect(() => {
+    if (!form.symbol && symbols && symbols.length) set('symbol', symbols[0].ticker)
+  }, [symbols]) // eslint-disable-line react-hooks/exhaustive-deps
+
   const set = (k: string, v: unknown) => setForm(f => ({ ...f, [k]: v }))
 
   const run = () => runBacktest(form as Record<string, unknown>)
@@ -74,43 +80,46 @@ export default function Backtest() {
             <div className="section-title">Configuration</div>
             <div className="space-y-3">
               <div>
-                <label className="text-xs text-slate-500 mb-1 block">Underlying</label>
+                <label className="text-xs text-slate-500 mb-1 block">Underlying (Saxo-linked)</label>
-                <div className="flex flex-wrap gap-1 mb-1">
+                {!symbols?.length ? (
-                  {SYMBOLS.slice(0, 7).map(s => (
+                  <div className="text-xs text-slate-600 border border-slate-700/40 rounded px-2 py-1.5">
-                    <button
+                    Aucun instrument lié à Saxo — Config → Instruments Watchlist.
-                      key={s}
+                  </div>
-                      onClick={() => set('symbol', s)}
+                ) : (
-                      className={clsx('px-1.5 py-0.5 rounded text-xs border', {
+                  <select
-                        'bg-blue-600 border-blue-500 text-white': form.symbol === s,
+                    value={form.symbol}
-                        'border-slate-700 text-slate-500': form.symbol !== s,
+                    onChange={e => set('symbol', e.target.value)}
-                      })}
+                    className="w-full bg-dark-700 border border-slate-700 rounded px-2 py-1.5 text-sm text-white focus:outline-none focus:border-blue-500"
-                    >
+                  >
-                      {s}
+                    {symbols.map(s => (
-                    </button>
+                      <option key={s.ticker} value={s.ticker}>{s.ticker} — {s.name}</option>
-                  ))}
+                    ))}
-                </div>
+                  </select>
-                <input
+                )}
-                  type="text"
-                  value={form.symbol}
-                  onChange={e => set('symbol', e.target.value.toUpperCase())}
-                  className="w-full bg-dark-700 border border-slate-700 rounded px-2 py-1.5 text-sm text-white focus:outline-none focus:border-blue-500"
-                />
               </div>
 
               <div>
                 <label className="text-xs text-slate-500 mb-1 block">Strategy</label>
-                {STRATEGIES.map(s => (
+                <div className="max-h-64 overflow-y-auto pr-1 space-y-1">
+                {(strategies ?? []).map(s => (
                   <button
                     key={s.key}
                     onClick={() => set('strategy', s.key)}
-                    className={clsx('w-full text-left px-2 py-1.5 rounded mb-1 text-xs border transition-all', {
+                    className={clsx('w-full flex items-center justify-between gap-2 text-left px-2 py-1.5 rounded text-xs border transition-all', {
                       'bg-blue-600/20 border-blue-500/60 text-blue-300': form.strategy === s.key,
                       'border-slate-700/40 text-slate-400': form.strategy !== s.key,
                     })}
                   >
-                    {s.label}
+                    <span>{s.label}</span>
+                    <span className={clsx('text-[10px] px-1 rounded shrink-0', {
+                      'bg-blue-500/20 text-blue-300': form.strategy === s.key,
+                      'bg-slate-700/40 text-slate-500': form.strategy !== s.key,
+                    })}>
+                      {s.n_legs}j
+                    </span>
                   </button>
                 ))}
+                </div>
               </div>
 
               <div>
@@ -221,7 +230,7 @@ export default function Backtest() {
 
               {/* Equity curve */}
               <div className="card">
-                <div className="section-title">Equity curve — {form.symbol} {STRATEGIES.find(s => s.key === form.strategy)?.label}</div>
+                <div className="section-title">Equity curve — {form.symbol} {(strategies ?? []).find(s => s.key === form.strategy)?.label}</div>
                 <div className="text-xs text-slate-500 mb-3">
                   Final capital: <span className="text-white font-bold">{typed.final_capital.toFixed(2)}€</span>
                   {' '}(initial: {form.capital}€ · P&L: {typed.total_pnl >= 0 ? '+' : ''}{typed.total_pnl.toFixed(2)}€)
@@ -262,8 +271,8 @@ export default function Backtest() {
                         <th className="text-left pb-2">Entry</th>
                         <th className="text-left pb-2">Exit</th>
                         <th className="text-right pb-2">Entry price</th>
-                        <th className="text-right pb-2">Strike</th>
+                        <th className="text-left pb-2">Legs</th>
-                        <th className="text-right pb-2">Premium</th>
+                        <th className="text-right pb-2">Net premium</th>
                         <th className="text-right pb-2">Exit price</th>
                         <th className="text-right pb-2">P&L</th>
                         <th className="text-right pb-2">Capital</th>
@@ -272,13 +281,16 @@ export default function Backtest() {
                     <tbody>
                       {typed.trades.map((t, i) => {
                         const pnl = t.pnl as number
+                        const netPremium = t.net_premium as number
                         return (
                           <tr key={i} className="border-b border-slate-700/20 hover:bg-dark-700/50">
                             <td className="py-1">{t.entry_date as string}</td>
                             <td className="py-1">{t.exit_date as string}</td>
                             <td className="py-1 text-right font-mono">${(t.S_entry as number).toFixed(2)}</td>
-                            <td className="py-1 text-right font-mono">${(t.K as number).toFixed(2)}</td>
+                            <td className="py-1 font-mono text-slate-400">{legsSummary(t.legs as LegRow[])}</td>
-                            <td className="py-1 text-right font-mono">${(t.premium as number).toFixed(4)}</td>
+                            <td className="py-1 text-right font-mono">
+                              {netPremium >= 0 ? '' : '+'}{(-netPremium).toFixed(2)}{netPremium >= 0 ? ' débit' : ' crédit'}
+                            </td>
                             <td className="py-1 text-right font-mono">${(t.S_expiry as number).toFixed(2)}</td>
                             <td className={clsx('py-1 text-right font-mono font-bold', pnl >= 0 ? 'positive' : 'negative')}>
                               {pnl >= 0 ? '+' : ''}{pnl.toFixed(2)}€
@@ -299,7 +311,7 @@ export default function Backtest() {
               <div className="text-center">
                 <History className="w-10 h-10 mx-auto mb-3 opacity-20" />
                 <div className="text-sm">Configure and run a backtest</div>
-                <div className="text-xs mt-1">yfinance data — full history available</div>
+                <div className="text-xs mt-1">Prix sous-jacent yfinance (historique complet) · options simulées Black-Scholes</div>
               </div>
             </div>
           )}