To hedge the swap position, we need to calculate the net dollar duration exposure:

First swap (pay fixed):

• Notional: $420 million
• Duration: 4.433
• Dollar duration = 420,000,000 × 4.433 = $1,861,860,000
• Since it's pay fixed, this represents a short position in bonds

Second swap (receive fixed):

• Notional: $385 million
• Duration: 7.581
• Dollar duration = 385,000,000 × 7.581 = $2,918,685,000
• Since it's receive fixed, this represents a long position in bonds

Net dollar duration: Long position - Short position = 2,918,685,000 - 1,861,860,000 = $1,056,825,000

This means the trader has a net long duration exposure of $1,056,825,000.

To hedge this using Eurodollar futures:

• Each Eurodollar futures contract has a DV01 of $25
• The DV01 of the position = Dollar duration × 0.0001 = 1,056,825,000 × 0.0001 = $105,682.50

Number of contracts = DV01 position / DV01 per contract = 105,682.50 / 25 = 4,227.3

Since the trader has a net long duration exposure, they need to sell Eurodollar futures to hedge. Therefore, the trader should buy 4,227 Eurodollar contracts.