* Euronext equity trading volumes up 31 pct in month

* European equities attract big investment inflows again

By Atul Prakash and Blaise Robinson

LONDON/PARIS, Feb 5 (Reuters) — Trading desks and exchange operators enjoyed roller-coaster moves on financial markets last month, but it is not clear whether the welcome volatility can make up for cost-cutting by banks and brokers.

Recent data from European stock-market operators Euronext and Deutsche Boerse showed cash equity volumes rose in January, following increased volumes in November and December. Market swings and rising inflows contributed to the pick-up.

Exchange operators like Deutsche Boerse are benefiting hugely from the uptick in stock and market volatility, with growing interest in exchange-traded funds and hedging reflected in rising futures and options volumes on the exchanges, said Edmund Shing, a global equity fund manager at BCS Asset Management.

That is welcome news for equities desks at investment banks as they release 2014 results — Switzerland’s UBS and France’s Societe Generale are due to report next week — but the gains might fizzle out.

It’s too soon to say, said John Colon, consultant at Greenwich Associates, which provides market intelligence to financial services. There have been several false dawns when volumes seemed to be picking up or were expected to pick up.

European stock market operator Euronext recorded a 31 percent jump in daily transaction value on its cash order book for January compared with the same month a year ago, extending gains over the past few months. Rival Deutsche Boerse saw a similar trend.

Euronext enjoyed its most active day in terms of transaction value in nearly four years on Dec 19. Some 15.98 billion euros ($18.3 billion) of its cash products traded, including equities, exchange-traded funds, warrants and certificates.

The recovery in volumes at Euronext — the operator of the Paris, Amsterdam, Brussels and Lisbon Bourses — is also visible in the average number of transactions, up 25 percent in January.

Deutsche Boerse, the operator of the German stock market, said the order book turnover for its main trading platforms stood at 148.5 billion euros in January, up about 19 percent from a year earlier.

Beyond the volatile swings in currency and commodities markets, global asset managers are also betting that a European Central Bank bond-buying plan will spark a multi-year share rally.

Last week, European equities enjoyed $5.1 billion of net investment inflows, the biggest weekly amount since December 2013, according to data from BofA Merrill Lynch Global Research.

European stocks have attracted $7.2 billion in fresh money so far this year, despite the rise in volatility, a boon for stock market operators and brokers.

The shares of both Euronext and Deutsche Boerse higher in recent months. Euronext is up 63 percent since mid-October. Deutsche Boerse has jumped 37 percent in the past four months. (Additional reporting by Andreas Kroener in Frankfurt; Editing by Larry King)