Valuing a Cross-Currency Swap Settled in a Delivery Currency

Summary

The document asks how to value a quarterly swap whose fixed and floating interest amounts are calculated on a notional in one currency, while net payments are settled in another. It presents a proposed fixed-leg present value that multiplies the non-delivery-currency notional and fixed rate by a spot-to-forward exchange-rate ratio, then discounts using the delivery currency discount factor. The questions focus on why that discount curve is used and what the exchange-rate ratio represents.

No answer or derivation is included, so the expression cannot be confirmed from the document alone. The central modeling issue is the consistent conversion and discounting of cash flows: valuation depends on the settlement currency, the exchange-rate quote convention, and the market curves and collateral assumptions. The text supplies no floating-leg formula, contract details beyond payment frequency and currency roles, or market inputs. It therefore introduces a cross-currency swap valuation question but leaves both the formula’s accuracy and the economic interpretation of its FX adjustment unresolved.

Key ideas

• The swap calculates interest amounts in a non-delivery currency but settles net cash flows in a delivery currency.
• The proposed fixed-leg value uses a delivery-currency discount factor and a spot-to-forward FX ratio.
• The question asks how settlement currency determines the appropriate discounting framework.
• The meaning of the FX ratio depends on the exchange-rate quote and cash-flow conversion convention.
• The document provides no derivation or answer confirming the proposed valuation expression.

Tags

# Pricing of a non-standard swap contract


# Pricing of a non-standard swap contract












Here I have a swap product, where a fixed and floating interest rate will be applied on notional amount. Fixed and floating legs involves 2 currencies, one of them is delivery currency (e.g. USD) and other currency is non-delivery currency (e.g. EUR) and pay that non-delivery currency (CCY-2) and receive also in non-delivery currency (CCY-2). Net cashflows will be settled in delivery currency (CCY-1). Payment frequency is quarterly.

In above arrangement, I was told that NPV for fixed leg is defined with following expression

$N \times \sum_{t=1}^{n} 0.25 \times K \times \frac{{FX}_{t=0}}{{FX}_{t}} DF \left(0 , t \right)$

Where $K$ is the fixed rate

$N$ is notional in CCY-2

$DF \left(0 , t \right)$ discount factor in delivery currency with tenor $t$

${FX}_{t}$ is Forward FX rate for CCY-1 / CCY-2

${FX}_{t=0}$ is spot FX rate

With this I am wondering in above expression to calculate the NPV of fixed leg is correct? I mainly have 2 fundamental question

- Why Discount factor need to be considered in Delivery currency

- What is the relevance of the expression $\frac{{FX}_{t=0}}{{FX}_{t}}$

Could you please help explaining the accuracy of above expression? If not then what would be the right expression?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.