Investors should hold on to shares of certain big-name restaurants despite lofty prices, some "Fast Money" traders argued Thursday.

Domino's Pizza shares spiked 13 percent on the day after strong earnings, and the stock has now climbed 19 percent this year. McDonald's stock, meanwhile, has climbed 20 percent in the last year.

"I think you have got to stay with it," trader Guy Adami said of Domino's. He also urges investors to stick with McDonald's shares.

Trader Tim Seymour agreed about McDonald's, saying its valuation looks more appealing than Domino's. Seymour's firm, Triogem Asset Management, owns McDonald's shares.

Adami believes shares of another burger chain, Jack in the Box, could tick higher after weakness. The stock has shed about 30 percent of its value in the last year.

Disclosures:

Tim Seymour

Tim Seymour is long AAPL, BAC, BBRY, DO, F, FCX, GM, GOOGL, INTC, JCP, NKE, SINA, T, TWTR, VZ, XOM. Tim's firm is long BABA, BIDU, CLF, KO, MCD, PEP, PF, SAVE, SBUX, VALE, WMT,YHOO, short HYG, IWM.

Dan Nathan

Dan is long PFE buy-write, long TWTR, long UUP March calls, long GE May 28 puts, long JPM April puts, long XLP March put spread, long XRT March puts, long XLB March puts, long HD put butterfly, long QQQ puts, long INTC March/April put spread

Karen Finerman

Karen is long BAC, C, FL, GOOG, GOOGL, JPM, LYV, KORS, M, SEDG, SPY calls, URI, she is short SPY. Her firm is long ANTM, AAPL, BAC, C, C calls, FINL, FL, GOOG, GOOGL, JPM, JPM calls, KORS, LYV, M, MOH, NRF, PLCE, URI, her firm is short IWM, MDY, SPY. Karen Finerman is on the board of GrafTech International.

Guy Adami

Guy Adami is long CELG, EXAS, GDX, INTC, Guy Adami's wife, Linda Snow, works at Merck.