What happened

Shares of Tesla (TSLA -4.02%) are up sharply again on Thursday, extending a bullish run for the stock this week. It rose as much as 4.5% at one point in the trading day but shares are still up 2.3% as of 1:10 p.m. EST today.

The electric-car maker's stock may be rising Thursday for a combination of reasons, including further momentum following news on Monday that the stock would soon be included in the S&P 500 and an analyst's recent move to set a $540 12-month price target for the growth stock.

In addition, CEO Elon Musk set big expectations for the company's upcoming software update for its "full self-driving" beta technology.

A Tesla vehicle with a license plate reading, Zero Emissions

The Tesla Model X. Image source: The Motley Fool.

So what

When discussing Tesla's beta for "full self-driving" technology, which requires drivers to be ready to take over the wheel and is available in only a limited number of vehicles, Musk wrote on Twitter Thursday morning, "Next week's [software] release is special." There will be a lot of "fundamental improvements, both important bug fixes & entire new areas of functionality," he said.

On a related note, Morgan Stanley analyst Adam Jonas' decision to upgrade his rating on the stock earlier this week was based largely on expectations that Tesla can continue to improve its self-driving technology, leading to a significant long-term monetization opportunity for the automaker. Investors may be starting to give Tesla's potential in software more weight in their expectations for the stock's long-term potential.

Shares are now up a total of 22% this week.

Now what

Major improvements to its Autopilot and self-driving features would strengthen the thesis for Tesla building a major revenue stream from software over time.

Though all Tesla vehicles come standard with the cameras and sensors that management believes can eventually enable full self-driving, customers can pre-pay for this functionality for $10,000 while also getting access to other enhanced driver-assist features. The automaker expects this price to increase substantially in the coming years. Even more, there's speculation Tesla could shift to a subscription model for its software.