Trading volumes in both derivative securities such as futures and options, as well as basic stocks, were more than 20 percent below year-ago levels in May for NYSE Euronext.

The biggest plunge: Trading in U.S. stocks, which dropped 45.5 percent from May 2010 levels, according to the operator of the New York Stock Exchange

The culprit in all cases: Comparison to … May 2010, when volumes were inflated by the sudden drop and resurgence in trading across futures, equities and other markets by the Flash Crash of May 6.

For May 2011, NYSE Euronext said its average daily volume of derivatives contracts, in all markets worldwide, was 10.6 million contracts. This was down 20.6 percent from a year ago.

The exchange operator attributed that to last year when there was “unseasonally strong trading volumes due to heightened market volatility driven by the sovereign debt crisis in Europe.

The emergent debt crisis in Greece helped stoke fears on May 6, when stocks plunged nearly 1,000 points at the worst point. The joint Securities Exchange Commission and Commodity Futures Trading Commission report on that day’s events noted that there was a “ nearly ten-fold increase in volume that occurred as prices in many securities rapidly declined.’’

Which is one backdrop to the NYSE’s report that European stock trading volume in May of this year was 22.0 percent below last year, but that trading in stocks in the U.S. this year was 45.5 percent below May of 2010.

Trading volumes in stocks in U.S. markets stayed at elevated levels for weeks after the May 6 Flash Crash.

Here’s what NYSE Euronext reported a year ago:

• NYSE Euronext’s global derivatives businesses (Europe and U.S. combined) averaged an all-time record 13.3 million contracts traded per day during the month of May 2010.

• On May 7, 2010, NYSE Liffe set a new exchange record for derivative contracts traded of 16.1 million contracts in a single day, well above the previous record of 14.9 million contracts recorded on May 6, 2010.

• NYSE Euronext European derivatives products ADV in May 2010 of 8.5 million contracts increased 51.5% compared to May 2009 and increased 24.6% from April 2010 levels. Total European fixed income products ADV in May 2010 of 3.4 million contracts increased 56.6% compared to May 2009 and increased 23.5% from April 2010. Total equity products ADV of 5.0 million contracts in May 2010 increased 48.8% compared to May 2009 and increased 26.0% from April 2010.

• NYSE Euronext U.S. equity options (NYSE Arca and NYSE Amex) ADV of 4.8 million contracts in May 2010 increased 90.3% compared to May 2009 levels and increased 20.2% from April 2010. NYSE Euronext’s U.S. options exchanges accounted for 26.0% of the total consolidated equity options trading in May 2010, up from 17.1% in May 2009 and up from the 25.3% recorded in April 2010.

• NYSE Euronext European cash products ADV of 2.0 million transactions in May 2010 increased 37.3% compared to May 2009 and increased 28.2% from April 2010.

• NYSE Euronext U.S. cash products (NYSE, NYSE Arca and NYSE Amex) handled ADV of 3.8 billion shares in May 2010 decreased 0.3% compared to May 2009, but increased 33.5% compared to April 2010. NYSE Euronext’s Tape A matched market share in May 2010 was 37.8%, the highest level since June 2009, up from 34.1% in April 2010.

There were a total of 21 trading days in Europe and 20 days in the U.S. in May 2010 compared to 20 trading days in both Europe and the U.S. in May 2009.