Merton / BSM Structural Equity Diagnostics

Single-file Flask web app for structural (Merton/BSM) equity analysis.
Given observable equity inputs, it calibrates firm assets ((V_A,\sigma_A)), computes deep risk/credit metrics, and produces scenario charts and a Monte-Carlo distribution for the per-share price at the analysis horizon (T).

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What it does

• Calibrates asset value and asset volatility from ((E,\sigma_E)) via a robust outer/inner bisection (no SciPy).
• Computes:
  • (d_1,d_2), distance-to-default ( \mathrm{DD}=d_2 ), PD (=\Phi(-d_2))
  • Delta and equity elasticity ( \Delta \cdot V/E )
  • Risky debt (D_0=V_A-E), credit spread (s) from (D_0=K e^{-(r+s)T})
  • Hazard proxy ( \lambda \approx \phi(d_2)/(\sqrt{T},\Phi(-d_2)) )
• Monte-Carlo under ( \mathbb{Q} ) for the terminal per-share price (P_T) with configurable paths.
• Dark UI with PD dial, scenario bars (5/50/95) and distribution histogram.

Security-conscious by default: strict CSP with per-request nonce, safe headers, no debug mode, and zero third-party Python deps beyond Flask and numpy (Chart.js is loaded from a CDN).

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Inputs (form)

• Stock Price (P_0) and Shares Outstanding (N_{\mathrm{sh}}) → equity value (E = P_0 N_{\mathrm{sh}})
• Total Debt Face (K) (millions), Cash (display only)
• Equity Volatility (\sigma_E) (%)
• Risk-free rate (r) (%) and Asset payout (q=\delta) (%)
• Horizon (T) (years)
• Monte Carlo Paths (1k–200k)

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Outputs (top panel)

• Calibrated (V_A) (firm assets), (\sigma_A)
• DD (d_2), PD (\Phi(-d_2)), status bucket (weak/moderate/strong)
• Elasticity ( \Delta \cdot V/E )
• Risky debt (D_0) and credit spread (s)
• Hazard proxy (\lambda)
• Per-share now (E/N_{\mathrm{sh}})

Charts

• Scenarios: 5% (“terrible”), 50% (baseline), 95% (“all goes well”) for (P_T)
• Histogram: empirical distribution of (P_T)

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Installation

Requires Python 3.9+ (tested with 3.10/3.11).

# clone your repo / copy these files into a folder
python -m venv env
source env/bin/activate          # Windows: env\Scripts\activate
pip install -r requirements.txt

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Run (local)

python StockAssessor.py
# opens http://127.0.0.1:5000

To run on a different port:

PORT=8000 python StockAssessor.py

Production (optional) behind a reverse proxy:

# inside the venv
gunicorn -w 2 -b 127.0.0.1:5000 StockAssessor:app

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How it works (at a glance)

• Equity as call on assets with carry $q$:

  $$ E = V e^{-qT}\Phi(d_1) - K e^{-rT}\Phi(d_2),\quad d_1=\frac{\ln(V/K)+(r-q+\tfrac12\sigma_A^2)T}{\sigma_A\sqrt{T}},; d_2=d_1-\sigma_A\sqrt{T}. $$

• Mapping $ \sigma_E = (\partial E/\partial V),(V/E),\sigma_A$.

• Calibration: bisection on $\sigma_A$ (outer), with a bisection on $V$ (inner) to match $E_{\text{obs}}$.

• Monte-Carlo (risk-neutral):

  $$ V_T = V_0 \exp!\big((r-q-\tfrac12\sigma_A^2)T + \sigma_A\sqrt{T}Z\big),; Z\sim\mathcal N(0,1),; P_T = \max(V_T-K,0)/N_{\mathrm{sh}}. $$

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Notes & Security

• The app sends no data off-box; Chart.js is fetched from JSDelivr. For offline use, vendor the JS file and change the <script> tag.
• Keep any Internet-facing deployment behind TLS and a reverse proxy. Add CSRF/auth if you enable stateful features.

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Troubleshooting

• “Could not bracket sigma_A for calibration” Inputs imply contradictory $E,\sigma_E$. Check $K$, $T$, or $\sigma_E$.
• “… out of bounds …” A field is outside allowed ranges; adjust the value.
• Blank charts You haven’t run Calibrate & Analyze yet, or the request failed validation.

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Project layout

MertonPredictor/
├── ReadMePic.png
├── StockAssessor.py
└── requirements.txt

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This tool is for research/education. It is not investment advice.

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# `requirements.txt`

```txt
# minimal, reproducible
Flask==3.0.0
numpy==1.26.4

# optional: for production serving (not used when running python StockAssessor.py)
gunicorn==21.2.0

If you prefer unpinned deps, swap the first two lines for:

Flask>=3.0,<4
numpy>=1.24,<3

Want a “Download report (CSV/PNG)” button next? I can add it without touching your calibration logic.