Sir James, who recently had to step down as deputy chairman of the Financial Services Authority (FSA) after allegations about his role in the collapse of HBOS, had jointly bought the flat in the heart of the New Town with his then employer, Halifax, for 496,000 in 2001. In September 2007, he paid 337,500 to HBOS for its 50 per cent share of the Thistle Street property, reflecting a value of 675,000 – an increase of only 36 per cent.
However, HBOS's own house-price index said property in Edinburgh city centre would have gone up 104 per cent between 2001 and 2007 – valuing the flat at closer to 1.01 million on that basis.
The estate agency Rettie also said that prices rose by 104 per cent over the period and, following Nationwide's index, that would have placed the value of the penthouse flat at more than 1.1 million. One leading Scottish property adviser told The Scotsman that Sir James had certainly got a bargain by paying only 337,500.
He said: "I wonder if there was a proper valuation done on the flat when he bought his share from HBOS?
"If the house would have been valued at 1 million, he should have paid 500,000. It seems he got a real bargain."
The bank claims an independent valuer said the penthouse was worth 675,000. The bank also said that Sir James had paid for half the flat in 2001, and that the 337,500 he paid in 2007 represented payment for the half he did not own.
In total, the former HBOS chief would have spent about 585,000 to own the property.
According to the Registers of Scotland, the penthouse, along with a garage in South West Thistle Street, was sold by the property developer Sundial Properties for 496,000 in 2001.
The deeds show the new owner was the bank, through a trustee company called BLP 2001-29, and Mr Crosby on a 50/50 ownership basis.
The penthouse became the Crosby residence in Edinburgh following the merger of Bank of Scotland with Halifax, of which Crosby had been the chief executive in 2001.
The married father of four also kept his home, Glendevon House in Harrogate, Yorkshire.
Six years later – and only a month before he was announced as the new deputy chairman of the FSA – Sir James became the outright owner of the flat.
The deal has brought calls for a review of the "happy" perks directors of failed banks have received.
Sir James enjoys a 10 million pension pot from his former employer, despite the bank revealing record losses last month. Many suggest he was behind a some of HBOS's risky lending that led to it being taken over by Lloyds Banking Group.
The deal took place just over a year after he had resigned from the board of HBOS and handed the reigns to his young protg, Andy Hornby.
According to experts consulted by The Scotsman, under company law, if the deal took place more than a year after Sir James resigned, neither he nor HBOS would have to make anything about the deal public.
One wealth management specialist said that, as valuations were complex and relied on many factors, it would be possible to get a valuation slightly lower than the market.
He said: "The valuation should be a demonstrably arms-length transaction. The difficulty is that valuations are very subjective. If you get a friendly valuer, it could be on the low side. It could happen and sometimes it does."
Stewart Hosie, the SNP MP for Dundee East, said: "HBOS has just lost 10 billion and much of it in bad property deals. The man who was their chief executive until 2006 has pretty much made its only risk-free property investment.
"But these allegations do beg more questions than answers. How many other executives that trashed their banks have been in receipt of similar happy arrangements?"
A source close to Sir James said he had left the details of the transaction to the bank and argued it was commonplace for company directors locating to Edinburgh to make similar arrangements or to stay in hotels at company expense:
The source went on: "HBOS secured the independent valuation and told him what he needed to pay for his half, and he paid it."
The 2007 deed transferring ownership was signed in July 2007. It was signed not only by the HBOS company secretary, Harry Baines, but also by the bank's chief executive, Andy Hornby.
Mr Baines, along with Jo Dawson, the group risk director, were the only HBOS board members to survive the takeover of the bank by Lloyds and to land roles at the newly formed Lloyds Banking Group.
The deed was later signed by Sir James and his wife, Una, who is listed as a joint owner of the property.
That took place on 10 September, 2007, and was witnessed by the Crosbys' nanny, Susan Clarkson.
The property, which the developers said boasts "expensive Bulthaup kitchens and Villeroy and Boch bathrooms as well as French oak and natural limestone floors" also includes a mezzanine floor.
The sale in 2007 that cost the Crosbys 337,500 also included the garage, which was described by estate agents as "a luxury for the New Town".