Explanation

To calculate the value of the equity swap, we need to find the value of both legs:

1. Fixed Leg (Receive Fixed):

• Fixed rate: 4.5%
• Notional: $1,000,000
• Annual payments: $1,000,000 × 4.5% = $45,000

Remaining payment dates: 0.5 years, 1.5 years, and 2.5 years

Present value of fixed payments:

• 0.5 years: $45,000 × 0.973236 = $43,795.62
• 1.5 years: $45,000 × 0.911162 = $41,002.29
• 2.5 years: $45,000 × 0.888889 = $40,000.01

Total PV of fixed leg = $43,795.62 + $41,002.29 + $40,000.01 = $124,797.92

2. Equity Leg (Pay Equity):

• Index decreased from 100 to 98 (2% decrease)
• Equity return = (98 - 100)/100 = -2%
• Equity payment = $1,000,000 × (-2%) = -$20,000

Present value of equity payment:

• PV = -$20,000 × 0.973236 = -$19,464.72

3. Swap Value: Value = PV(Fixed Leg) - PV(Equity Leg) Value = $124,797.92 - (-$19,464.72) = $124,797.92 + $19,464.72 = $144,262.64

However, this is not matching any options. Let me recalculate using the correct approach:

Correct Approach: The swap value = PV(Fixed Leg) - PV(Equity Leg)

PV(Equity Leg) = Notional × (Current Index/Initial Index - 1) × PV factor for next reset = $1,000,000 × (98/100 - 1) × 0.973236 = $1,000,000 × (-0.02) × 0.973236 = -$19,464.72

PV(Fixed Leg) = Fixed payment × Sum of PV factors = $45,000 × (0.973236 + 0.911162 + 0.888889) = $45,000 × 2.773287 = $124,797.92

Swap Value = $124,797.92 - (-$19,464.72) = $144,262.64

But this doesn't match the options. Let me check if we need to consider the initial swap value:

At initiation, swap value = 0 Current value = PV(Fixed Leg) - PV(Equity Leg)

Actually, the correct calculation should be: Swap Value = PV(Fixed Leg) - Notional × (Current Index/Initial Index) × PV factor for next reset

PV(Equity Leg) = $1,000,000 × (98/100) × 0.973236 = $953,771.28

Swap Value = $124,797.92 - $953,771.28 = -$828,973.36

This still doesn't match. Let me use the standard equity swap valuation:

Value = Notional × [PV(Fixed Payments) - (Current Index/Initial Index) × PV factor for next reset]

PV(Fixed Payments) = $45,000 × (0.973236 + 0.911162 + 0.888889) = $124,797.92

Value = $1,000,000 × [($124,797.92/$1,000,000) - (98/100) × 0.973236] = $1,000,000 × [0.12479792 - 0.95377128] = $1,000,000 × [-0.82897336] = -$828,973.36

This doesn't match the options either. Given the options, the closest is A: $-6,721, which suggests there might be a different interpretation or the question has specific assumptions.