How Currency Swaps Are Priced

Pricing a currency swap means valuing two sets of future cash flows in two different currencies and comparing them on a common basis. At inception, dealers normally set the contract so that the value is approximately zero to both sides, ignoring transaction costs and credit adjustments. After inception, the mark-to-market changes as discount curves, benchmark expectations, FX rates, and basis spreads move.

For DFOL, students do not need full quant-library implementation. They do need to understand the pricing logic well enough to identify what drives fair value and why the mark-to-market changes over time.

The Inception Objective

When a new currency swap is struck, the quoted fixed rate or spread is chosen so that:

• the present value of one leg
• equals the present value of the other leg

after both are expressed in a common valuation currency.

Conceptually:

This is the same high-level idea as an interest rate swap, but with one additional complication: the legs are in different currencies.

Main Inputs to Pricing

The value of a currency swap depends on:

• the notional amount in each currency
• current spot or agreed exchange relationships
• the fixed coupon, if any
• projected floating rates on any floating leg
• discount factors for each currency
• any cross-currency basis spread
• whether principal is exchanged at inception and maturity

Students should remember that there is no single all-purpose discount curve for both legs. Each currency has its own term structure.

Discounting the Two Legs

If a leg is denominated in Canadian dollars, it should be discounted using appropriate Canadian discount factors. If a leg is denominated in U.S. dollars, it should be discounted using U.S. discount factors.

In current market practice, modern discounting intuition is tied to overnight-rate frameworks such as:

• CORRA in Canadian dollars
• SOFR in U.S. dollars

That does not mean every exam question becomes a model-building exercise. It means students should not fall back on outdated benchmark assumptions when the question is about current-market pricing.

Fixed-Leg Valuation

The fixed leg is straightforward once the coupon is known:

Where:

• N is the notional
• K is the fixed coupon
• \alpha_i is the accrual fraction
• P(0,t_i) is the discount factor to payment date t_i

If principal is exchanged at maturity, the discounted principal repayment must also be added to the valuation of that leg.

Floating-Leg Valuation

The floating leg requires projected future benchmark cash flows. Market participants typically use forward curves to estimate those floating payments.

Conceptually, the steps are:

1. project future benchmark fixings
2. calculate expected coupon amounts
3. discount those projected amounts in the leg’s own currency

For a newly reset floating leg, the value is often close to par under standard assumptions. As time passes and curves move, the floating leg’s market value changes.

Converting to a Common Valuation Currency

Because the two legs are in different currencies, they must be expressed in a common valuation currency before the values can be compared.

One conceptual way to write the foreign-currency leg in domestic terms is:

Where:

• CF_i^{F} is the foreign-currency cash flow
• D_F(0,t_i) is the foreign-currency discount factor
• X_i represents the relevant FX conversion assumption

The exact implementation can vary, but the key exam idea is stable: each leg is valued in its own currency first, then translated onto a common basis.

Cross-Currency Basis Matters

Currency swap pricing is not just spot FX plus two domestic curves. The market may require an additional cross-currency basis spread to reflect supply, demand, funding pressures, and balance-sheet conditions across currencies.

Students do not need a full basis-curve construction process, but they should understand the point:

• if one currency is structurally more in demand for swap funding
• the quoted spread may adjust to reflect that imbalance

Ignoring cross-currency basis can produce a misleading valuation.

    flowchart LR
	    A["Domestic discount curve"] --> D["Leg valuation"]
	    B["Foreign discount curve"] --> D
	    C["FX and basis inputs"] --> D
	    D --> E["Common-currency present value"]

Why the Mark-to-Market Changes

After inception, the swap’s value can move because:

• interest-rate curves shift
• expected floating coupons change
• FX rates move
• basis spreads widen or tighten
• the remaining maturity shortens

This is why a swap that began at zero can later have meaningful positive value to one side and negative value to the other.

Common Pitfalls

• discounting both legs with the same curve
• assuming spot FX alone determines value
• ignoring the role of cross-currency basis
• using outdated benchmark assumptions for modern pricing
• confusing fair value at inception with mark-to-market after inception

Key Takeaways

• Currency swap pricing compares the present value of two currency legs on a common valuation basis.
• Each leg must be discounted using the appropriate curve for its own currency.
• Floating legs require projected benchmark cash flows, while fixed legs are valued from known coupons.
• FX conversion and cross-currency basis are central to the valuation.
• The swap’s mark-to-market changes after inception as rates, FX, and basis move.

Sample Exam Question

What is the clearest reason a currency swap cannot be priced by looking only at the fixed coupon and spot exchange rate?

• A. Because no discounting is needed
• B. Because both legs also depend on discount curves, future floating rates, and basis effects
• C. Because currency swaps are always exchange-traded
• D. Because principal is never exchanged

Correct Answer: B. Because both legs also depend on discount curves, future floating rates, and basis effects

Explanation: Currency swap valuation depends on the full discounted cash-flow structure of both legs, not just the coupon and current spot FX rate.