There are definitely connections, but mostly for the simple reason we can credit the city's entire existence to the business climate in the Netherlands.

In the early 17th century the Dutch brand of imperialism focused on controlling overseas trade, meaning their colonial settlements were often mainly hybrid military/trading outposts. The New Netherland colony basically falls under this category, although there's some conversation around its exact long-term purpose. Officially, it was run by the government-chartered West India Company with the aim of protecting trade interests in North America. However, some colonists wanted it to be more than a series of trading posts and saw value in a more typical settler colony that would take over Indian territory (while theoretically converting and assimilating the Indians) to establish a larger, permanent Dutch presence on the continent.

What's clear is Dutch merchants and farmers found de facto freedom to engage in all sorts of profit-seeking enterprises in New Netherland (working both inside and outside Company rules) and that the colony differed in fundamental ways from, for example, the neighboring religious colony in New England to the north. 17th-Century Amsterdam attracted many religious refugees and merchants of varying backgrounds from across northern Europe and that pluralistic, relatively "tolerant" society was replicated in New Netherland.

It's true that the stock exchange in Amsterdam predated similar European institutions in London and Paris that would become prominent later. But it would be wrong to view the New York Stock Exchange as a direct successor. There was quite a lag between the time the Dutch ceded control of the colony to the English in 1664 and when New York began to stand out as a center for securities trading in the mid 18th century.

In between we have to account for the influence of the English who found themselves in possession of a port city in a central position between their other colonies, situated on a river with deep access into the continent. Unsurprisingly, the acquisition attracted all sorts of enterprising individuals from Britain and its colonies who arrived to take advantage of the location, the natural resources, the city's commercial culture and its existing trade connections (in particular to the Caribbean), both legitimate and otherwise.

Under English rule trade expanded quickly as the population grew and the government officially centralized the colony's import and export activity in the city itself. With growing trade came a growing number of taverns and coffee houses to serve travelers along with the city's now numerous insurance dealers, brokers, and bankers of all types. And it was in these coffee houses in particular that the first semi-formalized trading of stocks began to take place around the 1730s. Business has been conducted over drinks wherever and whenever business has existed, but coffee houses as proto-stock exchanges were a British import, as much as anything.

It wouldn't be until the 1790s that stock trading received written guidelines in New York and it would be the 1820s, during another period of trade expansion, before the city surpassed other northeastern cities as the nation's premier securities market.

So while New York's modern stock market is as British and American as it is Dutch, its rise couldn't have happened if the Dutch hadn't handed over their unique colony that was almost ready-made for global commerce.

Related, I had a brief conversation a few months back about some of the other ways Dutch rule influenced NYC from the perspective of civil liberties. The books I mention there are my main sources for this.