Perhaps surprisingly, the local share market has skyrocketed today providing Australian investors with a much-needed breath of fresh air.

Although the Dow Jones and NASDAQ indices recorded falls of 1.6% and 0.1% respectively overnight, the pair had fallen 3.5% and 3.6% respectively during the session as markets continued to sweat on China’s slowing growth and a further decline in oil prices.

However, the local S&P/ASX 200 (Index: ^AXJO) (ASX: XJO) has managed to shake it off, surging 1.5% higher to 4915 points.

In yet another surprise, BHP Billiton Limited (ASX: BHP) is one of the companies leading the charge higher. The miner’s London-listed shares crashed 7.7% overnight, while Rio Tinto Limited’s (ASX: RIO) London-listed shares fell 4.1%, yet the pair have risen 1.8% and 3.3% locally.

Australia and New Zealand Banking Group (ASX: ANZ) shares are also on the rise again after a sharp fall on Wednesday, up 0.9%, while Commonwealth Bank of Australia (ASX: CBA), National Australia Bank Ltd. (ASX: NAB) and Westpac Banking Corp (ASX: WBC) have all gained more than 1%.

Even Woodside Petroleum Limited (ASX: WPL) has risen 0.6% today, despite the energy producer flagging impairments worth between US$1 billion and US$1.2 billion. The after-tax impact is expected to be between US$700 million and US$850 million.

Although it seems likely that the market will remain volatile for some time yet, it is clear that some investors are becoming more confident that there are bargains to be had on the Australian share market.

As scary as it may be, investors should at least remain on the lookout for high-quality companies trading at reasonable prices. Often these periods of severe market volatility can create fantastic buying opportunities.

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Motley Fool contributor Ryan Newman has no position in any stocks mentioned. Unless otherwise noted, the author does not have a position in any stocks mentioned by the author in the comments below. You can follow Ryan on Twitter @ASXvalueinvest.

The Motley Fool Australia has no position in any of the stocks mentioned. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy. This article contains general investment advice only (under AFSL 400691). Authorised by Bruce Jackson.