Sergei Kulik
⚠️ Working draft. This is an article in active development. Formulas, numbers, and conclusions may change as open issues are resolved — see TODO.md for what is known to be incomplete. Nothing here is investment advice.
A mathematical model of the "wheel" options strategy — repeatedly selling cash-secured puts on fundamentally sound assets, taking assignment when it comes, and selling covered calls until the stock is called away — framed as a stochastic inventory system. Put assignments are arrivals into an inventory of stock lots; call-aways are departures; the machinery of queueing theory answers how much stock the strategy really holds, how much capital it consumes, and when it stops being self-recycling.
The end product will be a LaTeX article for a general, numerate audience.
| Path | Contents |
|---|---|
sections/ |
The article, one Markdown file per section, numbered in reading order. 00-notation.md is the glossary and single source of truth for symbols. |
code/ |
Supplementary scripts. verify_examples.py recomputes every worked numerical example quoted in the text. |
TODO.md |
Open modeling and writing issues, cross-referenced from the sections. |
drafts/ |
Historical drafts. Superseded by sections/ — the initial draft contains a since-corrected P&L formula. |
Every worked example in the article is machine-checked:
python code/verify_examples.py
Python 3.8+, standard library only.
The article text is licensed under CC BY 4.0; the code under code/ is licensed under MIT. See LICENSE.md.
Tier 1 (the homogeneous approximation — all inventory lots share one recovery rate) is drafted. Tier 2 — depth-dependent recovery rates, the true stability condition, and the stable/metastable/unstable phase diagram — is planned; see sections/10-outlook.md.