As the share price falls delta falls towards zero. Delta may be used to construct a risk free hedge position, whereoverall wealth will not change with small changes in share price.
Theta measures the change in the option price as the time to expiry increases. The longer the time to expiry of an option, the greater its value. Theta may be used to estimate how much the value of an option will fall as time to maturity reduces.
Vega measures the change in option price as a result of a 1% change in the share price volatility or variance. As volatility increases, the value of both call and put options increases.
All three are of use to treasury managers when hedging their investments. As their values approach zero the hedged position will become unaffected changes in these variables.