Created to offer greater protection for investors, it is estimated that global banks and asset managers will have spent $2.1bn (£1.5bn) in order to comply with the 1.7 million paragraphs of rules.
"What we can see for our part is no glitches so far", Steven Maijoor, head of the European Securities and Markets Authority, told journalists on Wednesday.
Fixed income volumes were lower at 1000 GMT compared with their average at that time over the previous 30 days, according to data provider Trax, a subsidiary of MarketAxess that tracks around 65 per cent of all secondary market bond deals.
Europe's Markets in Financial Instruments Directive - Mifid II - is an attempt to provide greater protection to investors and shore up transparency throughout the financial system.
"The key thing to realise is MiFID II isn't done".
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Market nerves were eased by ESMA announcing measures just before Christmas to give companies more time to comply with some key requirements.
"For us the key element is that in the course of today's rules for the first time we see data of all financial instruments in the European Union, the so-called reference data", Maijoor said.
The open access model is the foundation of LCH, the world's largest clearing house for derivatives, whereas ICE and Eurex operate under a vertical model, meaning derivatives traded on their exchanges have to be cleared through their own CCPs.
Jeff Sprecher, CEO and chairman of ICE, has been an outspoken critic of MiFID II and open access, beliving the rules will stifle competition and favour only the incumbent clearing houses.
Among the changes, asset managers will now have to pay for the research that prompts their investment decisions, as regulators clamp down on potential conflicts of interest which could harm investors.