{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizzazione Interattiva delle Greche\n",
    "\n",
    "**Companion notebook per \"Trading con le Opzioni - Strategie Operative\"**  \n",
    "di Pierpaolo Marturano (Core Matrix S.r.l.)\n",
    "\n",
    "Questo notebook permette di visualizzare come cambiano le greche al variare di:\n",
    "- Prezzo del sottostante\n",
    "- Tempo a scadenza\n",
    "- Volatilità implicita\n",
    "\n",
    "Requisiti: `numpy`, `scipy`, `matplotlib`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Importa il modulo greche (deve essere nella stessa cartella)\n",
    "from greche import delta, gamma, theta, vega, vanna, volga, charm, bs_price\n",
    "\n",
    "plt.style.use('seaborn-v0_8-whitegrid')\n",
    "plt.rcParams['figure.dpi'] = 100\n",
    "plt.rcParams['font.size'] = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Parametri di Base\n",
    "\n",
    "Modifica questi parametri per esplorare diversi scenari:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# === PARAMETRI DA MODIFICARE ===\n",
    "S = 5500        # Prezzo attuale del sottostante (SPX)\n",
    "K = 5500        # Strike price\n",
    "T = 45 / 365    # Tempo a scadenza (45 giorni)\n",
    "r = 0.045       # Tasso risk-free (4.5%)\n",
    "sigma = 0.16    # Volatilità implicita (16%)\n",
    "\n",
    "print(f\"Sottostante: ${S}\")\n",
    "print(f\"Strike: ${K}\")\n",
    "print(f\"DTE: {T*365:.0f} giorni\")\n",
    "print(f\"IV: {sigma*100:.1f}%\")\n",
    "print(f\"Risk-free: {r*100:.1f}%\")\n",
    "print(f\"\\nPrezzo Call: ${bs_price(S, K, T, r, sigma, 'call'):.2f}\")\n",
    "print(f\"Prezzo Put:  ${bs_price(S, K, T, r, sigma, 'put'):.2f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Delta al variare del prezzo del sottostante"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "S_range = np.linspace(S * 0.85, S * 1.15, 200)\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
    "\n",
    "# Delta per diverse scadenze\n",
    "ax = axes[0]\n",
    "for dte in [7, 21, 45, 90, 180]:\n",
    "    T_i = dte / 365\n",
    "    delta_vals = [delta(s, K, T_i, r, sigma, 'call') for s in S_range]\n",
    "    ax.plot(S_range, delta_vals, linewidth=2, label=f'{dte} DTE')\n",
    "\n",
    "ax.axhline(y=0.5, color='gray', linestyle='--', alpha=0.5)\n",
    "ax.axvline(x=K, color='gray', linestyle=':', alpha=0.5)\n",
    "ax.set_title('Delta Call per Scadenza', fontweight='bold')\n",
    "ax.set_xlabel('Prezzo Sottostante ($)')\n",
    "ax.set_ylabel('Delta')\n",
    "ax.legend()\n",
    "ax.set_ylim(-0.05, 1.05)\n",
    "\n",
    "# Delta per diverse IV\n",
    "ax = axes[1]\n",
    "for iv in [0.10, 0.16, 0.25, 0.35, 0.50]:\n",
    "    delta_vals = [delta(s, K, T, r, iv, 'call') for s in S_range]\n",
    "    ax.plot(S_range, delta_vals, linewidth=2, label=f'IV={iv*100:.0f}%')\n",
    "\n",
    "ax.axhline(y=0.5, color='gray', linestyle='--', alpha=0.5)\n",
    "ax.axvline(x=K, color='gray', linestyle=':', alpha=0.5)\n",
    "ax.set_title('Delta Call per Volatilità', fontweight='bold')\n",
    "ax.set_xlabel('Prezzo Sottostante ($)')\n",
    "ax.set_ylabel('Delta')\n",
    "ax.legend()\n",
    "ax.set_ylim(-0.05, 1.05)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"Osservazione: con meno DTE o meno IV, il delta diventa più 'binario' (0 o 1).\")\n",
    "print(\"Questo spiega perché le 0DTE hanno un gamma esplosivo.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Gamma: dove è massimo?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
    "\n",
    "# Gamma per diverse scadenze\n",
    "ax = axes[0]\n",
    "for dte in [1, 7, 21, 45, 90]:\n",
    "    T_i = dte / 365\n",
    "    gamma_vals = [gamma(s, K, T_i, r, sigma) for s in S_range]\n",
    "    ax.plot(S_range, gamma_vals, linewidth=2, label=f'{dte} DTE')\n",
    "\n",
    "ax.axvline(x=K, color='gray', linestyle=':', alpha=0.5)\n",
    "ax.set_title('Gamma per Scadenza', fontweight='bold')\n",
    "ax.set_xlabel('Prezzo Sottostante ($)')\n",
    "ax.set_ylabel('Gamma')\n",
    "ax.legend()\n",
    "\n",
    "# Gamma ATM nel tempo\n",
    "ax = axes[1]\n",
    "dte_range = np.linspace(1, 90, 200)\n",
    "gamma_atm = [gamma(S, K, d/365, r, sigma) for d in dte_range]\n",
    "\n",
    "ax.plot(dte_range, gamma_atm, linewidth=2.5, color='#ef4444')\n",
    "ax.set_title('Gamma ATM nel tempo (esplode vicino a scadenza)', fontweight='bold')\n",
    "ax.set_xlabel('Giorni a Scadenza')\n",
    "ax.set_ylabel('Gamma')\n",
    "ax.invert_xaxis()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(f\"Gamma a 45 DTE: {gamma(S, K, 45/365, r, sigma):.6f}\")\n",
    "print(f\"Gamma a 7 DTE:  {gamma(S, K, 7/365, r, sigma):.6f}\")\n",
    "print(f\"Gamma a 1 DTE:  {gamma(S, K, 1/365, r, sigma):.6f}\")\n",
    "print(f\"\\nIl gamma a 1 DTE è {gamma(S, K, 1/365, r, sigma) / gamma(S, K, 45/365, r, sigma):.1f}x quello a 45 DTE!\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Theta: il decadimento temporale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
    "\n",
    "# Theta per moneyness\n",
    "ax = axes[0]\n",
    "for dte in [7, 21, 45, 90]:\n",
    "    T_i = dte / 365\n",
    "    theta_vals = [theta(s, K, T_i, r, sigma, 'call') for s in S_range]\n",
    "    ax.plot(S_range, theta_vals, linewidth=2, label=f'{dte} DTE')\n",
    "\n",
    "ax.axvline(x=K, color='gray', linestyle=':', alpha=0.5)\n",
    "ax.axhline(y=0, color='gray', linestyle='-', alpha=0.3)\n",
    "ax.set_title('Theta Call per Scadenza ($/giorno)', fontweight='bold')\n",
    "ax.set_xlabel('Prezzo Sottostante ($)')\n",
    "ax.set_ylabel('Theta ($/giorno)')\n",
    "ax.legend()\n",
    "\n",
    "# Decadimento del prezzo nel tempo\n",
    "ax = axes[1]\n",
    "dte_range = np.linspace(90, 0.5, 200)\n",
    "prices_time = [bs_price(S, K, d/365, r, sigma, 'call') for d in dte_range]\n",
    "\n",
    "ax.plot(dte_range, prices_time, linewidth=2.5, color='#0d5c4d')\n",
    "ax.fill_between(dte_range, prices_time, alpha=0.1, color='#0d5c4d')\n",
    "ax.set_title('Prezzo ATM Call nel tempo (theta decay)', fontweight='bold')\n",
    "ax.set_xlabel('Giorni a Scadenza')\n",
    "ax.set_ylabel('Prezzo ($)')\n",
    "ax.invert_xaxis()\n",
    "\n",
    "# Evidenzia l'accelerazione negli ultimi 21 giorni\n",
    "ax.axvline(x=21, color='#ef4444', linestyle='--', alpha=0.7, label='21 DTE')\n",
    "ax.legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"Il theta accelera negli ultimi 21 giorni → ecco perché il ciclo 45-21 DTE è ottimale.\")\n",
    "print(f\"Theta ATM a 45 DTE: ${theta(S, K, 45/365, r, sigma, 'call'):.2f}/giorno\")\n",
    "print(f\"Theta ATM a 7 DTE:  ${theta(S, K, 7/365, r, sigma, 'call'):.2f}/giorno\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Vega: sensibilità alla volatilità"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
    "\n",
    "# Vega per scadenza\n",
    "ax = axes[0]\n",
    "for dte in [7, 21, 45, 90, 180]:\n",
    "    T_i = dte / 365\n",
    "    vega_vals = [vega(s, K, T_i, r, sigma) for s in S_range]\n",
    "    ax.plot(S_range, vega_vals, linewidth=2, label=f'{dte} DTE')\n",
    "\n",
    "ax.axvline(x=K, color='gray', linestyle=':', alpha=0.5)\n",
    "ax.set_title('Vega per Scadenza ($/1% IV)', fontweight='bold')\n",
    "ax.set_xlabel('Prezzo Sottostante ($)')\n",
    "ax.set_ylabel('Vega ($/1% IV)')\n",
    "ax.legend()\n",
    "\n",
    "# Vega ATM nel tempo\n",
    "ax = axes[1]\n",
    "dte_range = np.linspace(1, 180, 200)\n",
    "vega_time = [vega(S, K, d/365, r, sigma) for d in dte_range]\n",
    "\n",
    "ax.plot(dte_range, vega_time, linewidth=2.5, color='#3b82f6')\n",
    "ax.set_title('Vega ATM nel tempo', fontweight='bold')\n",
    "ax.set_xlabel('Giorni a Scadenza')\n",
    "ax.set_ylabel('Vega ($/1% IV)')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"Il Vega cresce con la scadenza → le LEAPS sono più sensibili alla IV.\")\n",
    "print(f\"Vega ATM 7 DTE:   ${vega(S, K, 7/365, r, sigma):.2f} per 1% IV\")\n",
    "print(f\"Vega ATM 45 DTE:  ${vega(S, K, 45/365, r, sigma):.2f} per 1% IV\")\n",
    "print(f\"Vega ATM 180 DTE: ${vega(S, K, 180/365, r, sigma):.2f} per 1% IV\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Greche di Secondo Ordine: Vanna e Charm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n",
    "\n",
    "# Vanna\n",
    "ax = axes[0]\n",
    "for dte in [7, 21, 45, 90]:\n",
    "    T_i = dte / 365\n",
    "    vanna_vals = [vanna(s, K, T_i, r, sigma) for s in S_range]\n",
    "    ax.plot(S_range, vanna_vals, linewidth=2, label=f'{dte} DTE')\n",
    "\n",
    "ax.axvline(x=K, color='gray', linestyle=':', alpha=0.5)\n",
    "ax.axhline(y=0, color='gray', linestyle='-', alpha=0.3)\n",
    "ax.set_title('Vanna (dDelta/dSigma)', fontweight='bold')\n",
    "ax.set_xlabel('Prezzo Sottostante ($)')\n",
    "ax.set_ylabel('Vanna')\n",
    "ax.legend()\n",
    "\n",
    "# Charm (delta decay)\n",
    "ax = axes[1]\n",
    "for dte in [7, 21, 45, 90]:\n",
    "    T_i = dte / 365\n",
    "    charm_vals = [charm(s, K, T_i, r, sigma, 'call') for s in S_range]\n",
    "    ax.plot(S_range, charm_vals, linewidth=2, label=f'{dte} DTE')\n",
    "\n",
    "ax.axvline(x=K, color='gray', linestyle=':', alpha=0.5)\n",
    "ax.axhline(y=0, color='gray', linestyle='-', alpha=0.3)\n",
    "ax.set_title('Charm (variazione giornaliera del Delta)', fontweight='bold')\n",
    "ax.set_xlabel('Prezzo Sottostante ($)')\n",
    "ax.set_ylabel('Charm (/giorno)')\n",
    "ax.legend()\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "print(\"Vanna: spiega come i flussi dei dealer muovono il mercato vicino a scadenza.\")\n",
    "print(\"Charm: mostra quanto il delta 'scivola' ogni giorno senza movimento di prezzo.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. Dashboard Completa: tutte le greche a colpo d'occhio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "fig, axes = plt.subplots(2, 3, figsize=(16, 10))\n",
    "fig.suptitle(f'Dashboard Greche — Call {K} Strike, {T*365:.0f} DTE, IV={sigma*100:.0f}%',\n",
    "             fontweight='bold', fontsize=13)\n",
    "\n",
    "greeks_funcs = [\n",
    "    ('Delta', lambda s: delta(s, K, T, r, sigma, 'call')),\n",
    "    ('Gamma', lambda s: gamma(s, K, T, r, sigma)),\n",
    "    ('Theta ($/day)', lambda s: theta(s, K, T, r, sigma, 'call')),\n",
    "    ('Vega ($/1%)', lambda s: vega(s, K, T, r, sigma)),\n",
    "    ('Vanna', lambda s: vanna(s, K, T, r, sigma)),\n",
    "    ('Volga', lambda s: volga(s, K, T, r, sigma)),\n",
    "]\n",
    "\n",
    "colors = ['#10b981', '#ef4444', '#f59e0b', '#3b82f6', '#8b5cf6', '#ec4899']\n",
    "\n",
    "for ax, (name, func), color in zip(axes.flat, greeks_funcs, colors):\n",
    "    vals = [func(s) for s in S_range]\n",
    "    ax.plot(S_range, vals, linewidth=2, color=color)\n",
    "    ax.axvline(x=K, color='gray', linestyle=':', alpha=0.5)\n",
    "    ax.axhline(y=0, color='gray', linestyle='-', alpha=0.2)\n",
    "    ax.set_title(name, fontweight='bold')\n",
    "    ax.set_xlabel('Prezzo ($)')\n",
    "    ax.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8. Esercizio: confronta Call e Put\n",
    "\n",
    "Modifica il codice qui sotto per confrontare le greche di call e put sullo stesso strike:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# ESERCIZIO: prova a cambiare K, T, sigma e osserva come cambia il profilo\n",
    "K_test = 5500\n",
    "T_test = 30 / 365\n",
    "sigma_test = 0.20\n",
    "\n",
    "fig, axes = plt.subplots(1, 3, figsize=(15, 4))\n",
    "\n",
    "for ax, (name, func_call, func_put) in zip(axes, [\n",
    "    ('Delta', \n",
    "     lambda s: delta(s, K_test, T_test, r, sigma_test, 'call'),\n",
    "     lambda s: delta(s, K_test, T_test, r, sigma_test, 'put')),\n",
    "    ('Theta',\n",
    "     lambda s: theta(s, K_test, T_test, r, sigma_test, 'call'),\n",
    "     lambda s: theta(s, K_test, T_test, r, sigma_test, 'put')),\n",
    "    ('Rho',\n",
    "     lambda s: rho(s, K_test, T_test, r, sigma_test, 'call'),\n",
    "     lambda s: rho(s, K_test, T_test, r, sigma_test, 'put')),\n",
    "]):\n",
    "    call_vals = [func_call(s) for s in S_range]\n",
    "    put_vals = [func_put(s) for s in S_range]\n",
    "    ax.plot(S_range, call_vals, linewidth=2, label='Call', color='#10b981')\n",
    "    ax.plot(S_range, put_vals, linewidth=2, label='Put', color='#ef4444')\n",
    "    ax.axvline(x=K_test, color='gray', linestyle=':', alpha=0.5)\n",
    "    ax.axhline(y=0, color='gray', linestyle='-', alpha=0.2)\n",
    "    ax.set_title(name, fontweight='bold')\n",
    "    ax.legend()\n",
    "    ax.grid(True, alpha=0.3)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
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