PARIS, April 30 (Reuters) - Two Hong Kong-based traders at Societe Generale left the French bank late last year after the group uncovered a string of unauthorised bets made through derivatives, a source close to the matter said.

The bets, made via options contracts tied to Indian stock-market indices, did not exceed authorised trading amounts and led to no losses, the source said, but the traders were not authorised to carry them out.

The bank's risk-management systems failed to detect the trades because they were made in the morning and unwound in the afternoon every day, leaving no trace of any trade exceeding limits in the books, the source added.

In the event of a severe market downturn, the bets could have cost SocGen significant losses, the source said.

"Our strict control framework has allowed us to identify a one-off trading incident in 2023, which didn't generate any impact and led to appropriate mending measures," SocGen said in a written statement sent to Reuters, without elaborating.

Bloomberg News was first to report the trades and departures.

SocGen, which reports its first-quarter earnings on Friday, has made improving its risk controls a priority.

The bank's most infamous risk control failure resulted in billions of euros in losses in 2008, after bets by "rogue trader" Jerome Kerviel.

France's third-biggest listed bank has gone trough a series of restructurings since then, including at its investment bank, formerly led by current group CEO, Slawomir Krupa.

Krupa, who cut riskier activities at the division, has a tricky balancing act as CEO of SocGen, as he tries to improve returns for shareholders while minimising trading risks.

SocGen's investment bank has struggled in recent years, losing market share to rivals, and the bank's share price has underperformed even as European banking shares have soared to their highest since 2015.

SocGen's shares have risen 6% since the start of the year. They fell 12% in September on the day Krupa presented the bank's new strategic plan. (Reporting by Mathieu Rosemain; Editing by Susan Fenton)