In the meantime, however, Iran's economy is improving—and its stocks are absolutely booming. The Tehran Stock Exchange, which rose 130 percent in 2013, is up another 33 percent since November, when the so-called P5+1 group reached an interim accord with Iran. Trading volume broke records in December.

All parties involved continue to warn that serious differences remain in the talks, and hopes for a final deal by July have been called ambitious.

Iran and the United States, United Kingdom, France, Russia, China and Germany agreed on Thursday to a timeline and framework for further talks next month on restraining the Islamic state's nuclear ambitions. At the same time, United Nations inspectors have reported improved access to Iran's nuclear facilities.

As Iran's government and a group of global powers creep forward on talks about easing economic sanctions slapped on that country, the Iranian street is showing signs of breaking free from the economic stagnation that has crippled the country for years.

Turquoise Partners, a Tehran-based boutique investment firm, told CNBC that it's investing all of its assets in the Tehran Stock Exchange.

Ramin Rabii, managing director of Turquoise, said Thursday that "there are three reasons why the Tehran exchange is up: Shares are selling in a new reality of commodity and currency prices. There is more confidence in the market due to a reduction of political tensions after last year's election. And because people aren't putting their money into property, dollar and gold markets, which have been doing poorly, there is really no other place to put money right now. So it goes into the stock market."

The firm has $200 million under management, a large sum for a privately run, Iran-based firm.

"Right now there is a lot of interest from overseas," Rabii said. "I get several emails a week. Interest has picked up since the November deal was announced. However, at this stage, it is mostly exploratory."



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Most of that attention comes from Europe but there is interest from the United States as well, Rabii said. However, the firm has been telling Americans that, due to U.S. regulations, it is still virtually impossible for Americans to invest in Iran.

Turquoise says it invests only in companies that are not subject to European Union and United Nations sanctions. Its top holdings are in Iran's consumer sector and commodity companies, mostly in the copper and steel space.

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Despite the market's rise, there are lingering questions about the economy. Inflation has lowered somewhat, but it still comes in at a staggering 35 percent a year. Rabii said he's optimistic, however, that the new government understands the economy and that inflation will be in the 20 percent range next year as a result.

Unemployment is also relatively high: Government estimates put it at 12 percent. However that's much lower than many European countries that were caught up in the financial crisis.

Economists who follow Iran add that it has a young and well-educated population. Because jobs have been hard to come by, many young people have chosen to stay in school and earn higher degrees. Many analysts believe Iran will be eager to attract new foreign investment in order to create jobs for the up-and-coming segment of the population.