I think the thesis is that payments are under penatrated in Latin America/Brazil. Basically a country like China is basically a cashless economy and everyone pays by smart phone apps. Credit cards are even rarely used. The reason is because phones are (slightly) more convinient, and because they dont need to link up to a bank account and build up the network like a credit card, the network is built by people downloading the app and linking there accounts. Thus the main reason payment apps are superior is because compared to credit cards that charge 200-300 basis points to merchants, Alipay (i.e. ant financial) charges merchants 55 bps. Thus for a developing country that doesnt have a history of credit card usage, smart phone apps are much more attractive. Meanwhile despite only charging 55 bp, Alipay generates over 40 billion in revenue is worth 150 billion dollars. Brazil's population is 1/6 of Chinas, so conceivably if it gets the same penatration, it could be worth 25 billion dollars. If you want to compare it to paypal which probably covers a geographical area that skews developed countries and maybe 2.5x the pop of brazil, you have a valuation of 40 billion dollars. At the same time this comparison is somewhat faulty bc paypal charges credit card like fees to merchants compared to 55 BP for alipay which is likely what stone co will roughly charge.
other things going for it is it has the largest network in Brazil if I'm not mistaken, and so you have a virtuous flywheel with it having both the most number of merchants and consumers on the platform.
The bear case is the valuation is very steep at 25x revenue. Additionally its unclear how profitable Alipay/Ant finicial will be. Variable costs are low, but so is what it can charge merchants. Although it seems like Stone seems to have high margins. I'm not sure what competitors to stone look like, but Ant does compete with tencent, which may mean Stone is in a better position.