Buffett seized on this failing of Black-Scholes in a letter to Berkshire shareholders three years ago.
When we won there, they had Ryan Giggs, Paul Scholes and Dimitar Berbatov on the bench.
Giggs and Scholes both went close before Taylor's arrival, and a minute later, Sheringham's winner.
Paul Scholes, so influential for United in their prolonged triumphs under the Scot, joined him in retirement.
Scholes was left on crutches, while Rooney limped off in some discomfort just before the hour mark.
And United's misery was complete a minute before time when Scholes was dismissed for an unnecessary handball.
Far better, reckons Mr Scholes, if firms were to buy protection against liquidity risk in the market.
England resumed their pressure in the second half, with Scholes again central to much of the attacking play.
Frederick cautions that Black-Scholes underestimates the probability of big moves, like that freakish crash on Oct. 19, 1987.
Meanwhile, Manchester United midfielder Paul Scholes announced on Saturday that he will be retiring for the second time.
Scholes said the spectators who had planned to attend on the morning of 29 July would be compensated.
But with French full-back Patrice Evra marauding down the left, and Scholes pulling the strings, United were dominant.
England coach Glenn Hoddle paid tribute to Shearer and Scholes after the game.
Rooney and Manchester United team-mate Paul Scholes were sent off in a pre-season friendly against Porto and handed suspensions.
BBC: SPORT | Football | My Club | Man Utd | Ball condemns Rooney's FA threat
Paul Scholes gave United a first-half lead, with John O'Shea and Kieran Richardson were on target after the break.
BBC: SPORT | Football | Europe | Ferguson salutes maturing Man Utd
Mr Scholes favours relying less on VAR to calculate capital reserves against losses.
It was clear Ruud van Nistelrooy and Paul Scholes were more influential footballing figures in the Old Trafford pantheon.
And it was the Black-Scholes equation that opened up the world of derivatives.
First he pushed away Scholes' header from point-blank range on the half-hour mark as England finally managed to push forward.
Scholes looked certain to score as Le Saux, set up by Ince, whipped in a perfect cross from the left.
Scholes was sent off in the second half after he picked up a second yellow card following a clumsy tackle.
BBC: SPORT | Football | My Club | Man Utd | Rooney & Scholes lose ban appeals
Kleberson went close with a left-foot strike from the edge of the penalty area after a neat cutback from Scholes.
Carson failed to hold Gary Neville's drive and the alert Scholes was on hand to smash home the loose ball.
The Italian revealed he tried to persuade Manchester United midfielder Paul Scholes to come out of international retirement, but failed.
It was too little too late, though, with Paul Scholes sent off late on in a lacklustre showing from United.
Another priority is to get a better understanding of systemic risk, which Messrs Scholes and Thaler agree has been seriously underestimated.
But for Ian Stewart, the story of Black-Scholes - and of Long-Term Capital Management - is a kind of morality tale.
Manchester responded with two sharp chances for Yorke and Scholes, the first saved by Poom and the second going inches wide.
They were not marking to market, were not evaluating potential losses on a rolling basis and therefore were not using Black-Scholes.
But England had other heroes, with Manchester United duo Paul Scholes and David Beckham a potent creative driving force alongside Gerrard.
应用推荐