On October 29 1929, my grandfather was working on the floor of the New York Stock Exchange. "They told us to walk in the street instead of the sidewalk if we walked outside," he once told me. "People were throwing themselves out of windows."

He had cataracts and I couldn't see his eyes through his dark glasses while he reminisced. "There were so many orders coming on to the floor that we couldn't handle all the paperwork. They had to put us up in the Chelsea Hotel on 23rd street and we worked all night finishing all the work. We destroyed the room in a huge pillow fight."

He recounted the story in 1995 because I was about to move into the Chelsea for what turned into a three-year stay.

"James," my grandmother said. "Don't tell them that at the Chelsea. Maybe they'll charge you for what he did." For her, it was perfectly natural to think that nearly 80 years later, under new management, in the building where Sid Vicious killed Nancy Spungen and the poet Dylan Thomas is commemorated in a plaque, I would somehow be charged for an incident in which my grandfather had a pillow fight on the worst day of US stock market history.

That is because worrying is something many people do. They remember things that made them feel scared. So it is not surprising that whispers of the "Asian contagion" effect of 1997 or the dotcom bust of 2000 could be heard last week when volatility soared 64 per cent in a day, the Chinese stock market had its biggest drop in a decade (nearly 9 per cent) and US stock indices had their worst day since the terrorist attacks of September 11 2001.

As Barry Ritholz points out in his blog, The Big Picture, the 3 per cent drop in the US markets wiped out enough value in US dollars to equal the entire capitalisation of the Chinese markets.

So let's forget about the market. Just over a week ago, the Dow was at record highs. Sooner rather than later it will be there again. Forget about this middling volatility on the way from here to there. Let's find some good companies, with cheap stocks that could be acquired, given the massive liquidity in the hands of private equity firms, corporate coffers, venture capital firms, hedge funds and others.

InterDigital Communications. Does your cell phone ring? If so, you may be making use of a patent owned by IDCC and licensed by your cell phone manufacturer. Patent licensing results in choppy revenues and cash flows. But don't worry about IDCC. It has $300m in cash in the bank and had $300m in cash flows last year. Also, recurring licensees increased their payments to IDCC by 32 per cent year on year. The business is solid and its core customers are not going anywhere.

I would not be surprised if a company such as Qualcomm, with a $1.5bn enterprise value, swooped on little King of Prussia, Pennsylvania, and bought IDCC for just six times cash flows. And I am not the only one who thinks so. The company just maxed out its $200m share buy-back programme and extended it to $300m. And the super-value mutual fund Heartland Value owns its shares as does the hedge fund Renaissance Technologies.

Renaissance, run by Jim Simons, a former mathematics professor, is a quantitative hedge fund that has been up more than 30 per cent a year since its inception in the 1980s.

My guess is that Heartland Value and Renaissance like the heavy cash position and the lack of debt, indicating that even if the business model falters, it has enough in assets to turn round the business.

Heartland Value owns another stock that intrigues me: the enterprise software maker Actuate. The company has $60m in cash with no debt on its balance sheet. It had 146 per cent earnings growth year on year and trades at a forward price-to-earnings ratio of just 14. The market has left it behind.

Another company to check out that investors have shied away from is Cryptologic. It has been hit hard by recent US legislation that puts a complete clamp on all online gambling. Canada-based Cryptologic sells the software used by many offshore gaming sites.

Although the company's revenue and earnings have been hit severely by the new laws, it is worth noting that for five years it has been diversifying from onshore revenue. For instance, it just sold a licence for its online poker software to an offshore gambling site owned by Playboy.

With a $323m market capitalisation and $126m in cash, Cryptologic has an enterprise value of $196m. It is expected to earn $1.18 a share next year, giving it a forward price/earnings ratio of 20.

The super-deep-value investor Mohnish Pabrai recently disclosed in a Securities and Exchange Commission filing that he owns shares in Cryptologic. Pabrai is a very Buffett-esque investor; I profiled and interviewed him for my book Trade Like Warren Buffett (Wiley, 2005).

Pabrai also seems to like the steel companies, owning shares in IPSCO and Universal Stainless & Alloy Products.

When I was five years old my grandfather would draw me a house with windows, doors and chimneys. He would tell me how many brick lengths the bottom and sides needed, and how many brick lengths each window and door would take. Then he asked me how many bricks it would take to build the whole house. If I had trouble, he wouldn't get upset. He would simply say: "This is how you build a house, you know."

One brick at a time.