Problem $3.(25$p$)$

$($i$)(5$p$)$ Recall that the Delta of the option measures the rate of change of the theoretical option value with respect to changes in the underlying asset's price. $($It is the first derivative of the value of the option with respect to the underlying instrument's price.$)$ Using the Put$-$Call parity, show that the difference between the Delta of long position in European call option and the Delta of long position in the European put option is equal to $1.($Assume both options are on the same underlying, have the same strike, the same maturity, and the risk free rates are equal in both contracts.$)$

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