> ## Documentation Index
> Fetch the complete documentation index at: https://valuation-101.com/docs/llms.txt
> Use this file to discover all available pages before exploring further.

# Option Value

> Dilution-adjusted Black-Scholes valuation for employee stock options.

## Module: `lib/option_value.py`

Values outstanding employee stock options using a dilution-adjusted Black-Scholes model. The resulting value is subtracted from equity in the DCF equity bridge.

## Why dilution adjustment matters

Standard Black-Scholes assumes exercising one option doesn't affect the stock price. But when employees exercise millions of options, new shares are issued, diluting existing shareholders. The dilution-adjusted model accounts for this by reducing the per-option value based on the ratio of options to total shares.

## Key functions

### `option_value(stock_price, strike, maturity, volatility, risk_free, dividend_yield, shares, options_count)`

Computes the total value of all outstanding employee options.

**Parameters:**

* `stock_price` — current market price per share
* `strike` — weighted average exercise price
* `maturity` — weighted average years to expiration
* `volatility` — annualized stock price volatility (standard deviation)
* `risk_free` — risk-free rate
* `dividend_yield` — annual dividend yield
* `shares` — shares outstanding (basic)
* `options_count` — number of options outstanding

**Returns:** Total option value (float) to subtract from equity.

### `dilution_factor(shares, options_count)`

Computes the dilution adjustment: `shares / (shares + options)`.

### `black_scholes_call(S, K, T, r, sigma, q)`

Standard Black-Scholes call option pricing (before dilution adjustment).

## Data source

Option data (count, weighted average strike, weighted average maturity) is extracted automatically during the [parse-raw-data-to-filings](/docs/skills/parse-raw-data-to-filings) phase from XBRL tags and saved to `options_flag.json` in the ticker cache. If no option data is found in XBRL filings, the equity bridge skips the option deduction.