* FTSEurofirst 300 up 1.4 pct, Euro STOXX 50 up 1.5 pct
* Derivative contract expiry helps reduce selling pressure
* Car makers rally after positive sales figures
* European equity funds suffer record weekly outflows -Lipper
By Francesco Canepa and Blaise Robinson
LONDON/PARIS, Oct 17 (Reuters) - European stocks rebounded on Friday after their steepest two-day fall in more than a year, with car makers leading the pack after strong sales data.
Among the top gainers were Renault, up 2.8 percent and PSA Peugeot Citroen up 5.2 percent, boosted by data showing car sales in Europe rose 6.1 percent in September, the 13th straight month of growth in sales.
By 1036 GMT, the FTSEurofirst 300 index of top European shares had risen 1.4 percent to 1,263.32 points, after shedding 3.8 percent in the previous two sessions, their steepest fall since June 2013.
The euro zone's blue-chip Euro STOXX 50 index was up 1.5 percent, at 2,917.69 points.
Global equity markets have been recovering since U.S. data on Thursday showed initial jobless claims fell to their lowest in 14 years, and industrial output rose sharply in September.
Friday's session was very volatile, however, in part due to the expiry of derivative contracts, traders said.
"The looming expiry of the derivative contracts had forced brokers to manage the delta (hedging of the contracts), which accelerated the market's slump," the head of Paris-based Perceval Finance, Jean-Louis Cussac, said.
"We're limiting the damage now, but the market remains very vulnerable. A lot of hedge funds have been 'long' equities, 'long' oil and 'short' bonds, and this has added to the panic mood and brought us close to capitulation levels yesterday."
Traders and fund managers had bought Euro Stoxx 50 put options in a 3,100-2,900 points channel and brokers sold the underlying shares to hedge those contracts when the cash index dropped below those levels this week.
The month-long sell-off in European stocks has prompted U.S.-based investors to slash their exposure to Europe, according to data from Thomson Reuters Lipper.
A Lipper poll of 109 U.S.-domiciled funds invested in European stocks, which include exchange-traded funds' (ETFs) holdings, shows net outflows of $1.3 billion in the seven days to Oct. 15, the biggest weekly redemptions since Lipper started to monitor the data in 1992.
"We think sentiment and fund flow have exaggerated the recent sell-off, and although the fundamentals may have worsened a bit, the equity market has overshot," Barclays Capital analysts said.
"Economic growth expectations have come down a bit, and incoming data have disappointed, but the stock market appears to us to have overreacted," they said.
In this context, many fund managers were holding on to their equity holdings or or even increasing their equity positions, seeing value in shares after the recent slide in prices.
"I think markets will bounce back," Cazenove Capital Management's chief investment officer, Richard Jeffrey, said. "I don't think anything really fundamentally has changed."
On the downside, a warning from Rolls-Royce that it would not return to growth next year sent shares in the British engineering group down 12.3 percent.
Rolls, the world's No. 2 maker of aircraft engines behind U.S. group General Electric, blamed worsening economic conditions and tightening Russian trade sanctions for hitting next year's results. It said orders were being cancelled and delayed in its nuclear and energy and power systems businesses.
Shares in technology firm Gemalto tumbled 8.5 percent after Apple unveiled a new SIM card that will be installed in its iPads, sparking worries over the future of Gemalto's own smart chips for mobile phones, traders said.
Apple said on Thursday its new iPad Air 2 will allow subscribers to switch wireless carriers much more easily, by swiping an icon across the screen of the device. (Editing by Louise Ireland)