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; 98-bibliography.md is the same for references. |
code/ |
Supplementary scripts. verify_examples.py recomputes every worked numerical example quoted in the text. |
TODO.md |
Open modeling and writing issues, grouped by article part. |
DONE.md |
Completed work, resolved questions, and what is deliberately out of scope. |
drafts/ |
Historical drafts, superseded by sections/ — the initial draft contains a since-corrected P&L formula. Also tranche-record.md, the one living file there: the account's statements as they arrive, and the path of every headline figure across them. |
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.
The article is in four parts. Part I (setup) and Part II (one asset) are written: the model has a single state variable — a lot's depth below its own frozen call strike — and the entry law, holding time, standing inventory, returns, three stability boundaries and the capacity of an account with a finite balance all follow from that one random walk. Part III (portfolios and correlation) and Part IV (verification, the live account, outlook) are not yet written, and the abstract and prior-work survey are written last; see TODO.md.
A prior-work literature pass on 2026-07-31 confirmed the article's central economic claim from three independent directions, and reopened Part II with four outstanding items, all of them in the returns section. Two are corrections: the volatility risk premium is currently quoted at its index level where this model is single-name, and the one implied volatility the article carries has no tenor axis. Two are additions, including the article's first risk statistic. Until those close, treat the returns section's volatility-premium figures as under revision.