WASHINGTON — Mark Carney, chairman of the Financial Stability Board, urged leaders of the Group of 20 nations on Thursday to take more strides to strengthen the global financial system.

Carney, who is also the Governor of the Bank of England, pointed to three specific areas that global regulators should pursue further: ending "too-big-fail," reforming the shadow banking system, and revamping the derivatives market.

"If we are to eliminate the fault lines that underlay the global financial crisis, renewed attention and vigor is required from the G20 in these particular areas, as well as in finishing the job of building resilient financial institutions," Carney wrote in a five-page letter to G20 leaders, who are meeting in St. Petersburg.

Carney noted that significant progress has already been made by global regulators in strengthening the banking system. Since the financial crisis, institutions have built up capital and are providing credit and helping to support the economic recovery, he said.

He added that many banks, including the 28 institutions designated as globally systemically important banks, are already on course to meet new minimum capital and liquidity requirements ahead of the 2019 implementation deadlines.

Still, Carney said several institutions need to make more progress, and warned that in some cases, the adoption of new rules by different countries has been inconsistent.

"The G20 must stay the course in implementing standards," Carney wrote, singling out Indonesia and Turkey to implement their final Basel III rules as quickly as possible. "Others need to bring the rules fully into effect. All authorities should recognize that the strengthening in capital has been uneven and that some banks still require significant repair."

Far more worrisome, he said, are the inconsistencies in risk models by banks used to calculate their capital needs.

"This must be addressed for depositors, investors, clients and authorities to have full confidence in the strength of bank balance sheets and their resilience during a downturn," he wrote.

Carney pointed to the necessity of implementing remaining aspects of the Basel III package, including a proposed leverage ratio. The Basel Committee on Banking Supervision has agreed to reach a deal on the leverage ratio by early 2014.

Additionally, he said G20 leaders could also encourage their own banks to improve their risk disclosures.

On shadow banking, the governor noted that recommendations already endorsed by the G20 members have been submitted to address remaining risks in the system, including a policy framework to strengthen oversight and regulation of shadow banking entities.

While progress to end "too big to fail" is already underway, Carney and the FSB pointed to the additional need for legislative reforms in many countries when it comes to resolution planning.

"Several jurisdictions have made reforms, but further actions are needed to give authorities resolution powers and tools," the FSB wrote in a separate memorandum. "We therefore urge that all G20 countries change legislation as needed to meet the key attributes by end-2015."

The FSB also asked leaders of the G20 for their endorsement to take further measures to make cross-border institutions resolvable. The international body said a global approach is needed to ensure the adequacy of loss absorption capacity when it comes to resolving a bank, including the nature, amount and location within the financial group's structure.

They also said broadly structural reform measures at a national level could help to address the too big to fail problem by restraining excessive risk-taking and improving the resolvability of systemically important financial institutions.

Thirdly, they urged that regulatory gaps, such as the shadow banking system, should be closed with improved oversight.

"We must avoid leaving regulatory gaps, which could mean that, when regulations are tightened in one area, market participants simply move risky activities to less regulated sectors," the FSB wrote.

Lastly, they said further work is needed on making derivatives markets safer.

Efforts are underway to reform the derivatives markets by increasing transparency through requirements to trade on organized platforms and report transactions to trade repositories, the group noted.

"We are also reducing and more systemically controlling the exposures financial firms have to each other in this market, by ensuring that central counterparties are placed between the two participants in standardized transactions, by setting minimum capital and margin requirements," said the FSB.

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