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5 changes: 5 additions & 0 deletions .github/copilot-instructions.md
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Expand Up @@ -29,3 +29,8 @@ applyTo: '/**'
* Do not use em dashes (—) in documentation files or docstrings. Use colons, parentheses, or restructure the sentence instead.
* Math in documentation and docstrings uses `$...$` for inline and `$$...$$` or `\begin{equation}...\end{equation}` for block equations. Do not use `.. math::` or `:math:` (RST syntax).
* To rebuild doc examples run `uv run ./dev/build-examples` — runs all scripts in `docs/examples/` and writes their output to `docs/examples_output/`

## Package structure

* Strategy runtime markdown descriptions (read by `load_description()` at runtime) live inside the package at `quantflow/options/strategies/docs/` — they must be inside the package to be accessible when the library is installed
* mkdocs documentation pages live in `docs/api/options/` — do not mix these two locations
27 changes: 7 additions & 20 deletions notebooks/reference/glossary.md → docs/glossary.md
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---
jupytext:
text_representation:
extension: .md
format_name: myst
format_version: 0.13
jupytext_version: 1.16.6
kernelspec:
display_name: Python 3 (ipykernel)
language: python
name: python3
---

# Glossary

## Characteristic Function

The [characteristic function](../theory/characteristic.md) of a random variable $x$ is the Fourier transform of ${\mathbb P}_x$,
The [characteristic function](../theory/characteristic) of a random variable $x$ is the Fourier transform of ${\mathbb P}_x$,
where ${\mathbb P}_x$ is the distrubution measure of $x$.

\begin{equation}
Expand Down Expand Up @@ -47,24 +34,24 @@ Check this study on the [Hurst exponent with OHLC data](../applications/hurst).

## Moneyness

Moneyness is used in the context of option pricing and it is defined as
Moneyness, or log strike/forward ratio, is used in the context of option pricing and it is defined as

\begin{equation}
\ln\frac{K}{F}
\end{equation}

where $K$ is the strike and $F$ is the Forward price. A positive value implies strikes above the forward, which means put options are in the money and call options are out of the money.
where $K$ is the strike and $F$ is the Forward price. A positive value implies strikes above the forward, which means put options are in the money (ITM) and call options are out of the money (OTM).


## Moneyness Time Adjusted
## Moneyness Vol Adjusted

The time-adjusted moneyness is used in the context of option pricing in order to compare options with different maturities. It is defined as
The vol-adjusted moneyness is used in the context of option pricing in order to compare options with different maturities. It is defined as

\begin{equation}
\frac{1}{\sqrt{T}}\ln\frac{K}{F}
\frac{1}{\sigma\sqrt{T}}\ln\frac{K}{F}
\end{equation}

where $K$ is the strike and $F$ is the Forward price and $T$ is the time to maturity.
where $K$ is the strike and $F$ is the Forward price and $T$ is the time to maturity and $\sigma$ is the implied Black volatility.

The key reason for dividing by the square root of time-to-maturity is related to how volatility and price movement behave over time.
The price of the underlying asset is subject to random fluctuations, if these fluctuations follow a Brownian motion than the
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- Hurst: examples/hurst
- Supersmoother: examples/supersmoother
- Volatility Surface: examples/volatility-surface
- Glossary: glossary.md
- Contributing: contributing.md
- Bibliography: bibliography.md
markdown_extensions:
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