Shares of BJ's Wholesale Club Inc. stock soared almost 18 percent Thursday after a California private equity firm acquired a large stake in the Natick chain with plans to urge BJ's to go private. Green Equity Investors, a fund started by private equity firm Leonard Green & Partners, reported it has a 9.5 percent stake in BJ's, making it the second largest shareholder after FMR LLC, the parent company of Fidelity Investments. Leonard Green, which has investments in Whole Foods Markets Inc., Rite Aid Corp., and other retailers, said it bought the BJ's shares because it believed they were undervalued, according to a filing with the Securities and Exchange Commission. Green Equity, in the filing, said it plans to contact BJ's management 'to engage in a dialogue regarding potential options for enhancing shareholder value. These discussions may include a 'going-private' transaction, new financings (potentially through mortgage financings or sale leaseback transactions), or other similar transactions.' Shares of BJ's stock closed Thursday at $43.54, up 17.64 percent from the previous day. Michael Gennaro, chief operating officer of Leonard Green & Partners, declined to comment. BJ's said it had talked with Green Equity in the past but would not discuss speculation about plans to go private or other details from the filing. 'We have an obligation to run the business in a way that maximizes shareholder value for the long term,' said Cathy Maloney, BJ's vice president of investor relations. 'We work hard to provide our members with outstanding value while investing in our communities and our team members. We believe that this is the right strategy to increase shareholder value for the long term.' Analysts said the investment by Green Equity makes sense and there has been speculation for years that BJ's could be taken over by a private equity firm. 'We have long held a view that BJ's might be a candidate for private equity investment,' Neil Currie, a retail analyst for UBS Investment Bank, wrote in a report Thursday. 'We are interested to hear management's response.' Currie said BJ's is an attractive target for private equity because of the stability of its membership income, which accounts for roughly 80 percent of its operating income, strong cash flow, cash-rich balance sheet, and BJ's ownership of 34 percent of the stores. Moreover, BJ's management has 'meaningfully improved' operations at the Natick-based chain, though there is more to work on, especially through updating its information technology, Currie wrote. 