How do you value a fixed-for-fixed currency swap mid-life with a worked example?
I understand the basic idea of swapping principal and coupons in different currencies, but I get confused when trying to value a currency swap that's already partway through its life. Can someone walk through a concrete numerical example showing how exchange rate changes create value for one counterparty?
Valuing a currency swap mid-life is conceptually straightforward once you see it as two bond positions. Here's the step-by-step approach.
Setup:
Sunrise Bank entered a 5-year fixed-for-fixed currency swap 2 years ago:
- Pays: 3.0% annually on USD 50 million notional
- Receives: 2.0% annually on EUR 45 million notional
- At inception, the exchange rate was 1.1111 USD/EUR (50M / 45M)
Current Market Data (Year 2):
- Remaining life: 3 years
- USD discount rate: 4.5% (flat)
- EUR discount rate: 3.2% (flat)
- Current spot rate: 1.08 USD/EUR
Step 1: Value the USD Leg (Bond You Pay)
Cash flows: $1.5M coupon at years 3, 4, 5 plus $50M principal at year 5.
| Year | Cash Flow | PV Factor (4.5%) | PV |
|---|---|---|---|
| 1 | $1.5M | 0.9569 | $1.4354M |
| 2 | $1.5M | 0.9157 | $1.3736M |
| 3 | $51.5M | 0.8763 | $45.1295M |
| Total | $47.9385M |
Step 2: Value the EUR Leg (Bond You Receive)
Cash flows: EUR 0.9M coupon at years 3, 4, 5 plus EUR 45M principal at year 5.
| Year | Cash Flow | PV Factor (3.2%) | PV |
|---|---|---|---|
| 1 | EUR 0.9M | 0.9690 | EUR 0.8721M |
| 2 | EUR 0.9M | 0.9390 | EUR 0.8451M |
| 3 | EUR 45.9M | 0.9099 | EUR 41.7644M |
| Total | EUR 43.4816M |
Step 3: Convert EUR leg to USD
EUR 43.4816M x 1.08 = USD 46.9601M
Step 4: Net Value to Sunrise Bank
Value = Receive leg - Pay leg = $46.9601M - $47.9385M = -$0.9784M
Sunrise Bank is underwater because (a) USD rates rose (making its pay leg cheaper to replicate but the receive leg also dropped), and (b) the EUR weakened from 1.1111 to 1.08, reducing the USD value of EUR receipts.
The key insight for FRM: currency swaps carry both interest rate risk and FX risk, making them more complex than plain vanilla interest rate swaps.
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