Shares in Royal Mail closed at 489p on the company's first day of full trading on the stock exchange, up almost 3%.
It is the first day that people who bought shares through the government's website have been able to trade.
Royal Mail also confirmed that full time staff will receive 725 shares, worth £3,545, at Tuesday's close.
The government priced the shares at 330p each. The sharp rise since then has led to criticism that they were sold too cheaply.
However, Royal Mail chief executive Moya Greene told the BBC she thought the flotation was valued correctly.
Royal Mail staff are not allowed to sell their shares for at least three years.
After three years they will be allowed to sell 613 shares and the rest in 2017.Right price?
Private investors who applied for between £750 and £10,000 worth of shares received 227 shares, initially worth £749.10 at the 330p float price. Those who applied for more than £10,000 worth of shares received none.
However, some investors, who applied online or by post for the shares, have been unable to trade because they do not yet have a reference number needed to sell the stock.
The Department of Business told the BBC it did not have information on what proportion of people have their reference numbers so far.
The prospectus detailing the flotation process for Royal Mail said investors could have to wait until Thursday for their reference number if they applied for shares online, and up to a week if they applied by post.'Wonderful moment'
Business Secretary Vince Cable has insisted that the taxpayer has not been short-changed by the privatisation, and in an interview with BBC business editor Robert Peston, Royal Mail chief executive Moya Greene said she thought the flotation was valued correctly.
"I think the secretary for business has called that one properly. With this company, I think we have to look through today to the next six to nine months to see," said Ms Greene.
"We have climbed through a deep hole and we still have a long way to go, but it is a wonderful moment," she added.
However, Robert Peston said that if the government sale had been at today's price, taxpayers would have received an additional £900m, at least, and so MPs on the business select committee are to question Vince Cable and his City adviser Lazards on why they sold the shares at the price they did.
The privatisation of the 52.2% stake in the Royal Mail has also sparked anger from trade unions, who have argued that customers will receive a worse service as a result.
"The share price increase is making profits for wealthy private investors and faceless institutions - it's not bringing any money into Royal Mail," said Dave Ward, deputy general secretary of the Communication Workers Union.
On Wednesday, the union, which represents the majority of Royal Mail workers, will reveal the outcome of a strike ballot by postal workers over pay and working conditions.
BBC industry correspondent John Moylan says that in previous disputes of this nature and seriousness the union has moved quickly to announce at least a 24-hour national strike.