black-scholes-model.ipynb

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   "cell_type": "code",
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   "source": [
    "import math\n",
    "from scipy.stats import norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "S = 45  # Underlying Price\n",
    "K = 40  # Strike Price\n",
    "T = 2   # Time to Expiration\n",
    "r = 0.1 # Risk-Free Rate\n",
    "vol = 0.1 # Volatility (σ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "d1 = (math.log(S/K) + (r + 0.5 * vol**2)*T ) / (vol * math.sqrt(T))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "d2 = d1 - (vol * math.sqrt(T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = S * norm.cdf(d1) - K * math.exp(-r * T) * norm.cdf(d2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = K * math.exp(-r * T) * norm.cdf(-d2) - S * norm.cdf(-d1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The value of d1 is:  2.3178\n",
      "The value of d2 is:  2.1764\n",
      "The price of the call option is: $ 12.27\n",
      "The price of the put option is: $ 0.02\n"
     ]
    }
   ],
   "source": [
    "print('The value of d1 is: ', round(d1, 4))\n",
    "print('The value of d2 is: ', round(d2, 4))\n",
    "print('The price of the call option is: $', round(C, 2))\n",
    "print('The price of the put option is: $', round(P, 2))"
   ]
  }
 ],
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