Using Black Scholes to estimate the size of Divergence Loss / Impermanent Loss for AMMs
This is a short note on the relationship between option pricing, Black Scholes and Defi Automated Market Makers (“AMMs”). You can read more about it in the paper – but this paper is by now 50 pages and it is worth telling this story somewhat more concisely. I will go very short on some of the issues here to please do check in the paper for details. The relationship between AMMs and Black Scholes option pricing stems from the fact that AMMs ultimately are trading strategies.
The AMM Book production setup
This is the 3rd book I am writing – the first one was part of the PRMIA Handbook and the second one was my book on financial regulations, and every time I decided about 2 seconds after I started writing that writing in Word is not and option. For the PRMIA Handbook this was a no-brainer – I had to include a lot of formulas, and the old formula editor sucked even more than the current one, so it was clear that something like LaTeX was the only option.
Optimal fee levels for automated market makers
Working through the literature for the book I’ve read this article and the results intrigued me. The authors analyzed the fees earned by liquiditiy providers as a function of fee levels, and their result was surprising. Paraphrasing it slightly it reads When only considering arbitrage trades, the optimal fee level, ie the fee level with a maximum fee income for LPs, is as small as possible whilst not being zero