{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "87278d94",
   "metadata": {},
   "source": [
    "# The Merton Model from Scratch\n",
    "\n",
    "Companion notebook to [Module 4 — Structural Models](https://rodoslay.com/credit-models/04-structural-models) at **rodoslay.com**.\n",
    "\n",
    "What this notebook builds, using nothing but `numpy` and `scipy`:\n",
    "\n",
    "1. The Merton pricing formulas — equity as a call on the firm's assets, risk-neutral PD as $N(-d_2)$\n",
    "2. A worked example firm, priced end to end\n",
    "3. Sensitivity plots — what leverage and asset volatility each do to PD and spreads\n",
    "4. The **KMV-style inversion**: recovering unobservable asset value $V$ and asset volatility $\\sigma_V$ from observable equity data\n",
    "5. Risk-neutral vs. real-world PD\n",
    "\n",
    "Every function is a few lines. Run it top to bottom."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "52075bd0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-14T00:47:36.712765Z",
     "iopub.status.busy": "2026-07-14T00:47:36.712615Z",
     "iopub.status.idle": "2026-07-14T00:47:37.591203Z",
     "shell.execute_reply": "2026-07-14T00:47:37.589803Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "from scipy.optimize import fsolve\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (9, 5)\n",
    "plt.rcParams[\"axes.grid\"] = True\n",
    "plt.rcParams[\"grid.alpha\"] = 0.3"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3de13300",
   "metadata": {},
   "source": [
    "## 1. The model\n",
    "\n",
    "The firm's assets $V$ follow geometric Brownian motion with volatility $\\sigma_V$. The entire debt is one\n",
    "zero-coupon bond with face value $D$ maturing at $T$. Equity is a European call on $V$ with strike $D$:\n",
    "\n",
    "$$E = V\\,N(d_1) - D e^{-rT} N(d_2), \\qquad\n",
    "d_1 = \\frac{\\ln(V/D) + (r + \\sigma_V^2/2)T}{\\sigma_V \\sqrt{T}}, \\qquad d_2 = d_1 - \\sigma_V\\sqrt{T}$$\n",
    "\n",
    "The risk-neutral survival probability is $N(d_2)$, so **PD** $= N(-d_2)$.\n",
    "Debt value is what's left of the firm: $B = V - E$. From the debt value we get the continuously\n",
    "compounded yield $y = \\ln(D/B)/T$ and the **credit spread** $s = y - r$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ad18e6f0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-14T00:47:37.593570Z",
     "iopub.status.busy": "2026-07-14T00:47:37.593262Z",
     "iopub.status.idle": "2026-07-14T00:47:37.598782Z",
     "shell.execute_reply": "2026-07-14T00:47:37.597944Z"
    }
   },
   "outputs": [],
   "source": [
    "def merton(V, sigma_V, D, T, r):\n",
    "    \"\"\"Price the Merton firm. Returns a dict with all the quantities of interest.\"\"\"\n",
    "    sT = sigma_V * np.sqrt(T)\n",
    "    d1 = (np.log(V / D) + (r + 0.5 * sigma_V**2) * T) / sT\n",
    "    d2 = d1 - sT\n",
    "\n",
    "    E = V * norm.cdf(d1) - D * np.exp(-r * T) * norm.cdf(d2)   # equity = call option\n",
    "    B = V - E                                                   # debt = the rest of the firm\n",
    "    pd_rn = norm.cdf(-d2)                                       # risk-neutral PD\n",
    "    y = np.log(D / B) / T                                       # yield on the risky debt\n",
    "    spread = y - r                                              # credit spread\n",
    "\n",
    "    return {\"d1\": d1, \"d2\": d2, \"equity\": E, \"debt\": B,\n",
    "            \"pd_rn\": pd_rn, \"spread_bps\": spread * 1e4}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bddb8774",
   "metadata": {},
   "source": [
    "## 2. A worked example\n",
    "\n",
    "A firm with assets of 100, asset volatility 25%, owing 80 in one year, risk-free rate 4%.\n",
    "(The same default case as the interactive widget in the post — the numbers should match.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "dbc2390c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-14T00:47:37.600725Z",
     "iopub.status.busy": "2026-07-14T00:47:37.600552Z",
     "iopub.status.idle": "2026-07-14T00:47:37.605200Z",
     "shell.execute_reply": "2026-07-14T00:47:37.604462Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "d1                    :   1.1776\n",
      "d2 (distance to dflt) :   0.9276\n",
      "Equity value          :    24.78\n",
      "Debt value            :    75.22\n",
      "Risk-neutral PD       :   17.68%\n",
      "Credit spread         :    216.0 bps\n"
     ]
    }
   ],
   "source": [
    "out = merton(V=100, sigma_V=0.25, D=80, T=1.0, r=0.04)\n",
    "\n",
    "print(f\"d1                    : {out['d1']:8.4f}\")\n",
    "print(f\"d2 (distance to dflt) : {out['d2']:8.4f}\")\n",
    "print(f\"Equity value          : {out['equity']:8.2f}\")\n",
    "print(f\"Debt value            : {out['debt']:8.2f}\")\n",
    "print(f\"Risk-neutral PD       : {out['pd_rn']:8.2%}\")\n",
    "print(f\"Credit spread         : {out['spread_bps']:8.1f} bps\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5484247e",
   "metadata": {},
   "source": [
    "## 3. Sensitivities — the two levers that matter\n",
    "\n",
    "PD as a function of leverage, for several asset volatilities. Watch how volatility *creates*\n",
    "default risk even at moderate leverage — and how at low volatility the PD curve stays glued to\n",
    "zero until leverage gets extreme. This nonlinearity is the model's core message."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3e7bcdee",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-14T00:47:37.607002Z",
     "iopub.status.busy": "2026-07-14T00:47:37.606820Z",
     "iopub.status.idle": "2026-07-14T00:47:38.074699Z",
     "shell.execute_reply": "2026-07-14T00:47:38.073417Z"
    }
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1200x450 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "leverage = np.linspace(0.2, 1.2, 200)          # D / V\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4.5))\n",
    "\n",
    "for sig in [0.10, 0.20, 0.30, 0.45]:\n",
    "    pds = [merton(V=100, sigma_V=sig, D=100 * L, T=1, r=0.04)[\"pd_rn\"] for L in leverage]\n",
    "    ax1.plot(leverage, np.array(pds) * 100, label=f\"sigma = {sig:.0%}\")\n",
    "ax1.set_xlabel(\"Leverage D/V\"); ax1.set_ylabel(\"1y risk-neutral PD (%)\")\n",
    "ax1.set_title(\"PD vs leverage\"); ax1.legend()\n",
    "\n",
    "maturities = np.linspace(0.05, 10, 200)\n",
    "for L in [0.5, 0.7, 0.9]:\n",
    "    sp = [merton(V=100, sigma_V=0.25, D=100 * L, T=t, r=0.04)[\"spread_bps\"] for t in maturities]\n",
    "    ax2.plot(maturities, sp, label=f\"D/V = {L:.0%}\")\n",
    "ax2.set_xlabel(\"Maturity T (years)\"); ax2.set_ylabel(\"Credit spread (bps)\")\n",
    "ax2.set_title(\"Spread term structure\"); ax2.legend()\n",
    "\n",
    "plt.tight_layout(); plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46cc62ba",
   "metadata": {},
   "source": [
    "Note the right-hand panel: for healthy leverage the spread **collapses to zero at short maturities**\n",
    "— a diffusion needs time to travel to the default point. Real markets never price short spreads at zero,\n",
    "and that failure is exactly what motivates the reduced-form models of\n",
    "[Module 5](https://rodoslay.com/credit-models/05-reduced-form-models).\n",
    "\n",
    "## 4. The KMV inversion — from equity data to asset data\n",
    "\n",
    "In practice you never observe $V$ or $\\sigma_V$; you observe the **equity** value $E$ (market cap)\n",
    "and can estimate **equity volatility** $\\sigma_E$. The model gives two equations linking the\n",
    "observables to the unobservables:\n",
    "\n",
    "$$E = V N(d_1) - De^{-rT}N(d_2) \\qquad\\qquad \\sigma_E \\, E = N(d_1)\\,\\sigma_V\\, V$$\n",
    "\n",
    "(The second is Ito's lemma applied to $E(V)$: equity vol is asset vol amplified by the option delta\n",
    "and the leverage.) Two equations, two unknowns — solve numerically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "416a4b92",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-14T00:47:38.076849Z",
     "iopub.status.busy": "2026-07-14T00:47:38.076629Z",
     "iopub.status.idle": "2026-07-14T00:47:38.083551Z",
     "shell.execute_reply": "2026-07-14T00:47:38.082723Z"
    }
   },
   "outputs": [],
   "source": [
    "def solve_kmv(E_obs, sigma_E_obs, D, T, r):\n",
    "    \"\"\"Back out (V, sigma_V) from observed equity value and equity volatility.\"\"\"\n",
    "    def equations(x):\n",
    "        V, sigma_V = x\n",
    "        sT = sigma_V * np.sqrt(T)\n",
    "        d1 = (np.log(V / D) + (r + 0.5 * sigma_V**2) * T) / sT\n",
    "        d2 = d1 - sT\n",
    "        E_model = V * norm.cdf(d1) - D * np.exp(-r * T) * norm.cdf(d2)\n",
    "        sigE_model = norm.cdf(d1) * sigma_V * V / E_model\n",
    "        return [E_model - E_obs, sigE_model - sigma_E_obs]\n",
    "\n",
    "    # start from naive guesses: assets = equity + debt, asset vol = deleveraged equity vol\n",
    "    V0 = E_obs + D\n",
    "    sig0 = sigma_E_obs * E_obs / V0\n",
    "    (V, sigma_V), info, ier, msg = fsolve(equations, x0=[V0, sig0], full_output=True)\n",
    "    assert ier == 1, f\"solver failed: {msg}\"\n",
    "    return V, sigma_V"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "ad934db5",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-07-14T00:47:38.085626Z",
     "iopub.status.busy": "2026-07-14T00:47:38.085426Z",
     "iopub.status.idle": "2026-07-14T00:47:38.092498Z",
     "shell.execute_reply": "2026-07-14T00:47:38.092012Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Implied asset value V      :  102.65\n",
      "Implied asset volatility   :  16.66%\n",
      "Distance to default (d2)   :    3.38 sigmas\n",
      "Risk-neutral 1y PD         :   0.04%\n",
      "Round-trip check — model E :   45.00  (observed 45.0)\n"
     ]
    }
   ],
   "source": [
    "# Observables for a hypothetical listed firm (in $bn):\n",
    "E_obs, sigma_E_obs = 45.0, 0.38          # market cap 45, equity vol 38%\n",
    "D, T, r = 60.0, 1.0, 0.04                # KMV-style default point, 1y horizon\n",
    "\n",
    "V_hat, sigV_hat = solve_kmv(E_obs, sigma_E_obs, D, T, r)\n",
    "res = merton(V_hat, sigV_hat, D, T, r)\n",
    "\n",
    "print(f\"Implied asset value V      : {V_hat:7.2f}\")\n",
    "print(f\"Implied asset volatility   : {sigV_hat:7.2%}\")\n",
    "print(f\"Distance to default (d2)   : {res['d2']:7.2f} sigmas\")\n",
    "print(f\"Risk-neutral 1y PD         : {res['pd_rn']:7.2%}\")\n",
    "print(f\"Round-trip check — model E : {res['equity']:7.2f}  (observed {E_obs})\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6efa4e25",
   "metadata": {},
   "source": [
    "Sanity checks worth internalizing: implied assets ≈ equity + debt value (not face value — debt trades\n",
    "below par when risky), and implied asset vol is *well below* equity vol, because leverage amplifies\n",
    "asset moves into bigger equity moves. Equity is the levered, optioned view of the same firm.\n",
    "\n",
    "**What KMV does next** (and we won't replicate without their default database): compute the distance\n",
    "to default, then **throw away** the Gaussian mapping $N(-d_2)$ and look up the *empirical* default\n",
    "frequency of firms that historically sat at that DD. The Gaussian tail is too thin; the ordering is\n",
    "excellent, the levels are not."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "716ed819",
   "metadata": {},
   "source": [
    "## 5. Risk-neutral vs. real-world PD\n",
    "\n",
    "$N(-d_2)$ uses the risk-free rate $r$ as the asset drift — that's what arbitrage pricing requires.\n",
    "The *physical* PD replaces $r$ with the true expected asset return $\\mu > r$:\n",
    "\n",
    "$$\\text{PD}^{\\mathbb{P}} = N\\!\\left(-\\,\\frac{\\ln(V/D) + (\\mu - \\sigma_V^2/2)T}{\\sigma_V\\sqrt{T}}\\right)$$"
   ]
  },
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     "name": "stdout",
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     "text": [
      "  mu (asset drift) | physical PD | risk-neutral PD = 17.68%\n",
      "------------------------------------------------------------\n",
      "               4% |      17.68% |\n",
      "               7% |      14.74% |\n",
      "              10% |      12.15% |\n",
      "              13% |       9.89% |\n"
     ]
    }
   ],
   "source": [
    "def merton_pd_physical(V, sigma_V, D, T, mu):\n",
    "    dd = (np.log(V / D) + (mu - 0.5 * sigma_V**2) * T) / (sigma_V * np.sqrt(T))\n",
    "    return norm.cdf(-dd)\n",
    "\n",
    "# Back to the worked-example firm (V=100, sigma=25%, D=80), whose risk-neutral PD was 17.68%\n",
    "pd_rn_example = merton(V=100, sigma_V=0.25, D=80, T=1, r=0.04)[\"pd_rn\"]\n",
    "print(f\"{'mu (asset drift)':>18} | {'physical PD':>11} | risk-neutral PD = {pd_rn_example:.2%}\")\n",
    "print(\"-\" * 60)\n",
    "for mu in [0.04, 0.07, 0.10, 0.13]:\n",
    "    pd_p = merton_pd_physical(V=100, sigma_V=0.25, D=80, T=1, mu=mu)\n",
    "    print(f\"{mu:>17.0%} | {pd_p:>11.2%} |\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "76f04e7b",
   "metadata": {},
   "source": [
    "The higher the true drift, the further the physical PD falls below the risk-neutral one. The gap is\n",
    "the **price of default risk** — the same wedge that makes CDS-implied default probabilities run above\n",
    "historical default rates (Module 5's closing point).\n",
    "\n",
    "**Rules of use:** risk-neutral PDs for *pricing* (they already contain the risk premium);\n",
    "physical PDs for *risk management, capital, and expected loss*.\n",
    "\n",
    "## Exercises\n",
    "\n",
    "1. **Asset substitution, quantified.** Fix $V=100$, $D=80$, $T=1$, $r=4\\%$. Plot equity value and debt\n",
    "   value as functions of $\\sigma_V \\in [5\\%, 80\\%]$. Who gains from risk, who loses, and where is the\n",
    "   transfer steepest?\n",
    "2. **The equity floor.** Set $D=130$ (assets deeply below face value of debt). How much is the equity\n",
    "   still worth at $T=1$ vs $T=5$? Why does maturity act like volatility here?\n",
    "3. **First-passage intuition.** Black–Cox lets the firm default *before* maturity, the first time assets\n",
    "   touch a barrier. Simulate 10,000 GBM paths for the worked-example firm and estimate the first-passage\n",
    "   PD with the barrier at $D$. How much higher is it than the Merton (endpoint-only) PD?\n",
    "4. **Real data.** Pick a listed firm; take market cap, an equity vol estimate (e.g. 1y realized), and a\n",
    "   KMV default point (short-term liabilities + half of long-term). Run `solve_kmv`. Is the implied DD\n",
    "   plausible against its credit rating (Module 6's transition data gives you the mapping)?"
   ]
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