1. Educational purposes only

The models, calculators, charts, formulas and text on robilliard.com (together, “the models”) are provided to illustrate the mathematics in the book Circangle: π is Obsolete. They are for education only. Use of the models is acceptance that they are for educational purposes only and of the terms on this page.

2. Not for pricing or any financial decision

The models must not be used to price, value, trade, hedge, margin or manage the risk of any financial instrument, position or portfolio; for accounting, regulatory, capital or reporting purposes; or as the basis of any investment or commercial decision.

3. Not advice, and no regulated service

Nothing on this site is investment, financial, legal, tax or other professional advice, or a personal recommendation. Nothing on this site is an offer, invitation or inducement to buy or sell any investment or to engage in any investment activity. This site does not provide any regulated financial service in the United Kingdom, the United States or elsewhere. If you need advice, consult a suitably qualified and authorised professional.

4. Proof-of-concept models

The models are proofs of concept. They have not been calibrated to market quotes, checked for arbitrage across a volatility surface, or independently validated, and they may contain errors. Results are computed with numerical approximations in your browser and may differ from other implementations. Example inputs, including the Brent crude examples, are illustrative only and are not market data. Hypothetical or modelled results do not indicate future outcomes.

5. No warranty

The site and the models are provided “as is” and “as available”, without warranties or representations of any kind, express or implied, including any implied warranties of accuracy, completeness, merchantability, satisfactory quality, fitness for a particular purpose or non-infringement.

6. Limitation of liability

To the fullest extent permitted by law, James Robilliard will not be liable for any loss or damage of any kind, whether direct, indirect, special, incidental or consequential, including any trading or investment loss, loss of profit, revenue or data, arising out of or in connection with the site or any use of or reliance on the models, whether in contract, tort (including negligence), breach of statutory duty or otherwise. Nothing in this disclaimer excludes or limits any liability that cannot be excluded or limited under applicable law. Some jurisdictions do not allow the exclusion of certain warranties or the limitation of certain damages, so some of these exclusions may not apply to you, in which case liability is limited to the smallest extent permitted.

7. Your responsibility

You are solely responsible for how you use the models and for any decision you make. You use the site at your own risk.

8. Intellectual property

© 2026 James Robilliard. All rights reserved. The text, formulas, figures and code on this site are protected by copyright. Black–Scholes–Robilliard and the other model names refer to models described in the book. You may share links to the site freely.

9. Links and privacy

Links to Amazon and LinkedIn go to sites outside my control, and their own terms apply. This site sets no cookies and runs no analytics or tracking; everything is calculated in your browser and nothing you enter is sent anywhere. The hosting provider may keep standard server logs.

10. Governing law

This disclaimer is governed by the law of England and Wales, and the courts of England and Wales have non-exclusive jurisdiction. If any part of it is found unenforceable, the rest remains in effect. It may be updated at any time; the version on this page applies.