Time Warner said on Wednesday it had rebuffed Twenty-First Century Fox's roughly $80 billion bid, or $85 per share, in recent weeks over valuation and concerns that the Murdoch family will have too much power. But people familiar with Twenty-First Century Fox said Murdoch is determined to buy the rival media giant.

Hedge fund traders and options strategists said the traditional merger arbitrage trade - short Twenty-First Century Fox and buy Time Warner - played out when the news broke.

Arbitrageurs seek to profit on the difference in stock prices between an acquirer and the target. In a deal that involves the swap of stock, that generally involves buying the target's shares and betting the acquirer's will fall. Murdoch made a stock and cash offer for Time Warner.

But these traders said that the time for that bet may have passed. Time Warner's stock has risen 21 percent to $86.12, since the news broke. Twenty-First Century Fox has fallen nearly 7 percent.

"Fox shares will spike higher if this deal is killed or if Time Warner bids for something," making a defensive acquisition, one arbitrageur said. "Time Warner will also remain range-bound, unless there is a higher bid or it does something that destroys the process, or something to buy another company."

So investors who missed that window must now make bolder bets if they still want in on the trade.

Sources have said that Twenty-First Century Fox could see more than $1 billion in synergies from a deal.

One hedge fund manager said in his reckoning synergies from the deal could be as high as $1.5 billion, which would allow Twenty-First Century Fox to pay as much as $95 per share to $100 per share and still have a deal be substantially accretive to 2016 earnings.

The hedge fund manager said many arbitrageurs are remaining long in shares of Time Warner, given Murdoch's reputation as a tenacious dealmaker.

Murdoch, for example, overcame stiff resistance from some members of the Bancroft family to buy Dow Jones in 2007. But he did not raise his bid at the time.

"The key right now for me is, 'What is my downside?'" said one hedge fund trader. "The price on the table is not the right price. It's not going to get it done." The trader said he owns a relatively small position in Time Warner and is evaluating how -- and whether -- to place a bigger bet.

AN OPTION

One way to put less money on the line while betting that Twenty-First Century Fox will raise its bid is to buy Time Warner stock options. Activity in the options market already shows investors are optimistic that either a bidding war could occur or Murdoch could end up raising his initial offer.

There was substantial activity in Time Warner call options expiring in mid-August with a $90 strike price - bullish bets that the stock will hit that level by that expiration.

"For you to buy an August $90, you have to believe there's a higher bid in the next month here or an increased bid by him," said William Lefkowitz, chief options strategist at vFinance Investments.

There were also notable new positions taken in call options expiring in mid-October at the $95 and $100 strike prices, which also suggests a belief that shares will keep rising. Nearly 2,000 new contracts were purchased at the $100 strike price for October, according to Thomson Reuters data.

But the bid-ask spread in August options contracts is at a very wide range – between 40 and 60 cents for a number of contracts. That makes it more expensive to make such a bet. The better bet may be in the stock market, which has tighter spreads.

Arbitrageurs will usually play in the market with tighter spreads because of efficiency, said J.J. Kinahan, chief derivatives strategist at TD Ameritrade.

WHITHER HEDGES?

There are few other options at the moment to arbitrage this deal, traders said.

In a sign that investors think Fox shares have fallen as much as they will, short interest is muted.

As of Wednesday, short interest in Twenty-First Century Fox was around 2.8 percent of the outstanding shares, a relatively low amount, according to data firm Markit.

The credit default swaps market, another avenue to hedge or bet on the trade, may not work out either, one arbitrageur said.

"These names are great credits, so even if Fox levers up to do a deal, it won't widen much. I doubt there's much to be done in CDS on this one," the arbitrageur said.

Twenty-First Century Fox's 5-year CDS price jumped about 20 percent Wednesday to their highest since February, but they moved no further on Thursday and remain relatively low. Time Warner's dropped nearly 6 percent.

(Additional reporting by Dan Wilchins, Jennifer Ablan and Daniel Burns; Writing by Paritosh Bansal, editing by Peter Henderson)

By Soyoung Kim and David Gaffen