FAQ for
Arbitrage (2012) More at IMDbPro »

Perhaps Miller lied to protect Grant's father in a similar situation in the past.

Another possibility hinted at is that Grant's father became sick and died. Since Grant's father was Miller's driver, the two men spent much time together and probably knew each other intimately. Miller, being a philantropist, may have taken pity on Grant's father, payed for hospital bills and eventual funeral costs, something Grant and his mother could not afford. When Grant himself got into trouble with the law, Miller arranged for an attorney who got him of with a light sentence. In any case, Grant felt an overwhelming sense of gratitude, enough to protect Miller at high personal cost.