Equity Monte Carlo Simulator

讓任何AI代理都能在一次工具呼叫中，對股票或ETF執行嚴謹的蒙地卡羅預測。

文件

mcp-monte-carlo

Give any AI agent the power to run a serious Monte Carlo forecast for a stock or ETF — in one tool call.

This is an MCP (Model Context Protocol) server. Connect it once to Hermes, Claude Desktop, Cursor, or any MCP-capable agent, and the agent can download market history, fit a volatility model, simulate thousands of future price paths, and return percentiles, drawdowns, and risk probabilities — without you writing a single line of simulation code.

You:  "What does a bad year look like for SPY over the next 12 months?"
Agent → forecast_asset_monte_carlo("SPY")
      → EGARCH + skewed-t Monte Carlo (5,000 paths by default)
You ← JSON: price/return percentiles, vol, max drawdowns, loss probabilities

Why this matters

Large language models are excellent at reasoning and explanation. They are not engines for sampling fat-tailed returns under time-varying volatility. Left alone, an agent might invent plausible-looking percentiles or hand-wave “historical vol $\times\sqrt{T}$”.

This server closes that gap:

Without this MCP	With this MCP
Agent guesses ranges or quotes stale numbers	Agent calls a reproducible statistical pipeline
No consistent treatment of crashes / fat tails	Skewed-t innovations model skewness and fat tails
Constant-vol assumptions ignore clustering	EGARCH captures shock-driven, asymmetric volatility
Hard to compare 7-day vs 10-year risk	Same model, same paths, many horizons in one JSON

The agent stays in charge of interpretation and conversation. The MCP owns estimation and simulation.

What it does (pipeline)

Yahoo Finance (max history)
        │  adjusted daily Close
        ▼
  Log returns
        │
        ▼
  Fit EGARCH(1,1) + leverage  +  skewed-t shocks
        │  constant mean drift (historical mean)
        ▼
  Simulate N paths  (default 5,000) out to 10 years
        │
        ▼
  Summarize each horizon → percentiles, vol, MDD, probabilities

1. Data

Uses yfinance to pull the maximum available daily history. The Close field is already adjusted for splits and dividends, so returns are suitable for long-horizon compounding.

2. Returns and drift

Prices are converted to log returns:

r_t=\ln\left(\frac{P_t}{P_{t-1}}\right)

The mean model is constant: each simulated day has drift equal to the fitted historical average $\mu$. That is a simple, transparent assumption — not a crystal ball for future expected return.

3. Volatility: EGARCH with leverage

Equity volatility is neither constant nor symmetric:

Volatility clustering — turbulent days tend to follow turbulent days.
Leverage effect — large down moves tend to raise future vol more than equally large up moves.

This server fits EGARCH(1,1) with leverage ($p=1$, $o=1$, $q=1$) via the arch package. Conditionally, log-variance evolves roughly as:

\ln(\sigma_t^2)=\omega+\alpha\bigl(\lvert z_{t-1}\rvert-\mathbb{E}[\lvert z\rvert]\bigr)+\gamma z_{t-1}+\beta\ln(\sigma_{t-1}^2)

For equities, the leverage coefficient $\gamma$ is typically negative: a negative shock $z$ increases tomorrow’s volatility.

4. Shocks: skewed Student-t

Gaussian shocks understate crash risk. Standardized innovations are drawn from a skewed t distribution, so simulated paths can show:

fat tails (extreme moves more often than a normal),
skewness (asymmetric left/right risk).

5. Monte Carlo paths

Given the fitted parameters, the server simulates $N$ forward trajectories (n_paths; vectorized NumPy loop for stability out to multi-year horizons). Each path is a full price series; horizons are slices of those same paths so short- and long-term stats are coherent.

6. Horizons (trading days)

Label	Trading days	Rough calendar
`7d`	5	~1 week
`30d`	21	~1 month
`3m`	63	~3 months
`6m`	126	~6 months
`1y`	252	~1 year
`3y`	756	~3 years
`5y`	1260	~5 years
`10y`	2520	~10 years

Tools

`forecast_asset_monte_carlo(ticker, n_paths=5000)`

When to use: The user wants forward scenarios, risk ranges, or path statistics for a ticker (e.g. SPY, AAPL).

For each horizon, the JSON includes:

Price percentiles — 1, 5, 10, 25, 50, 75, 90, 95, 99
Return percentiles (%) — same grid, vs today’s price
Annualized volatility (%) — cross-sectional vol of path outcomes at that horizon
Max-drawdown percentiles (%) — peak-to-trough loss along each path up to that horizon
Probabilities — end below start, ±20% moves, max drawdown over 20%

n_paths defaults to 5000 (minimum 100). More paths → smoother percentile estimates, slower run.

`inspect_asset_model(ticker)`

When to use: Validate data quality or model sanity before (or instead of) a full forecast — enough history? sensible parameters? how fat are residual tails?

Returns history span, last price, fitted EGARCH + skew-t parameters, AIC/BIC, last conditional volatility (daily and annualized), and residual skewness / excess kurtosis.

Does not simulate paths. Prefer forecast_asset_monte_carlo for percentiles and drawdowns.

Requirements

macOS, Linux, or Windows
uv (recommended)
Python ≥ 3.12 (declared in pyproject.toml)
Network access (Yahoo Finance download)

Quick start (local)

cd /path/to/mcp-monte-carlo
uv sync

Smoke-test without MCP:

uv run python -c "
from server import run_inspect, run
import json
print(json.dumps(run_inspect('SPY'), indent=2))
print(json.dumps(run('SPY', 200)['horizons']['1y'], indent=2))
"

Run the MCP server on stdio:

uv run mcp-monte-carlo
# or, from a published clone / path:
uvx --from /path/to/mcp-monte-carlo mcp-monte-carlo

Connect an AI agent

Hermes Agent (`~/.hermes/config.yaml`)

Prefer uv run against a synced project (faster and more reliable than a cold uvx):

mcp_servers:
  mcp-monte-carlo:
    command: /opt/homebrew/bin/uv   # which uv  → paste absolute path
    args:
      - run
      - --directory
      - /ABSOLUTE/PATH/TO/mcp-monte-carlo
      - mcp-monte-carlo
    connect_timeout: 120
    timeout: 300

Then: hermes mcp test mcp-monte-carlo or /reload-mcp in a chat.

Cursor / Claude Desktop

{
  "mcpServers": {
    "mcp-monte-carlo": {
      "command": "uvx",
      "args": [
        "--from",
        "/ABSOLUTE/PATH/TO/mcp-monte-carlo",
        "mcp-monte-carlo"
      ]
    }
  }
}

Once published on GitHub, others can point --from at the repo URL or clone locally and use the same pattern.

Example agent prompts

“Inspect the EGARCH model for QQQ, then forecast with 2,000 paths.”
“For AAPL, what is the 5th percentile price in 1 year, and the probability of a >20% max drawdown?”
“Compare 1-year median and 95th percentile max drawdown for SPY vs TLT.”

Project layout

mcp-monte-carlo/
├── server.py          # MCP tools + EGARCH/skew-t Monte Carlo (single module)
├── pyproject.toml     # package metadata, deps, console entry point
├── uv.lock            # locked dependency versions
├── README.md
└── .gitignore

One Python file keeps the project easy to read, audit, and ship.

Model caveats (read this)

This is a research / educational risk tool, not investment advice and not a guarantee of future prices.

Past drift $\mu$ is not a forecast of expected return; long-horizon medians inherit that assumption.
EGARCH(1,1)+leverage and skewed-t are strong defaults for many liquid equities/ETFs — not universally “optimal” for every ticker.
Yahoo data quality and corporate actions can affect results; always check inspect_asset_model on unfamiliar symbols.
Extremely long horizons (5y–10y) compound model risk; treat tails as illustrative, not certainties.

License / authorship

Created by Alexandre Martins. Use and adapt freely for personal agents and learning; if you redistribute, keep attribution and these caveats visible.