- They put their house down as loan collateral.
- He put his house up as collateral for his business loan.
What's different between 'down' and 'up' in these sentences?
None. They both have the same meaning. The particles "up" and "down" can both signify the completion of an event or task, or the furtherance of an action.
Similarly you can run for congress or stand for parliament. Which to use will be determined by the local convention or audience.