Why is the value of a swap zero at inception and what does this imply?

Question

AcadiFi · Accepted Answer

At inception, a dealer prices the fixed rate so PV(fixed leg) = PV(floating leg), leaving the swap with zero mid-market value to both counterparties. This is simply the no-arbitrage pricing condition — if either party paid upfront cash, there would be an arbitrage opportunity exploiting mispriced legs.

However, zero value applies to the mid-market theoretical rate. In practice, dealers like Quinwood Capital Markets quote bid-ask around mid: for a 5-year USD IRS with mid at 4.1850%, Quinwood might bid 4.1800% (dealer pays fixed) and offer 4.1900% (dealer receives fixed). The 1 basis point half-spread compensates for hedging costs, CVA/DVA adjustments, and initial margin funding.

When Calderwood Pension executes at 4.1900% (paying fixed to Quinwood), the swap has small negative MTM for Calderwood immediately — roughly 0.5bp × DV01 × notional. For $100M 5-year with DV01 ≈ $4,500 per bp, that's ~$2,250 cost.

```mermaid
flowchart TD
  A[Mid-market rate] --> B[Dealer quote bid ask]
  B --> C{Client side?}
  C -->|Pays fixed| D[Executes at offer]
  C -->|Receives fixed| E[Executes at bid]
  D --> F[Small negative MTM]
  E --> F
```

Implications: (1) Large corporates pay narrower spreads due to competition; (2) long-dated and exotic swaps carry wider spreads for CVA; (3) post-inception, valuation depends on curve shifts — the swap accumulates positive or negative MTM driving collateral flows.

Why is the value of a swap zero at inception and what does this imply?

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