Insider trading has been illegal for most Americans since the Securities Act was passed in 1933.
It was extended to cover US government officials in 2012, although to date no-one has been prosecuted under the law.
Paul Oudin, a professor who specialises in financial regulation law at the ESSEC Business School, says the rules are difficult to enforce.
“The financial authorities will not carry out a prosecution if they can’t figure out who the source of information is,” says Oudin.
None of the US financial authorities contacted by the BBC acknowledged any of the allegations of insider trading.
“You can have massive trades on a financial instrument that clearly show that someone was privy to what Donald Trump was about to declare,” says Oudin.
“Yet there is a strong chance that no-one will be prosecuted,” he adds.
Charts by Tommy Lumby
Clarification 23 April: This article was amended to give further details about movements in the oil price and to make clear that the price on 9 March dropped a further 14% after President Trump said the war was almost complete.