Introduction to Cross-currency swap Valuation

Cross-currency swaps (CCS) are a type of derivative instrument that allows two parties to exchange cash flows in different currencies. One party will typically be exposed to a risk of currency fluctuations, while the other party will be looking to take advantage of those fluctuations.

To value a CCS, you need to calculate the present value of the future cash flows in each currency. This can be done using a discounted cash flow (DCF) analysis. The discount rate you use will depend on the riskiness of the underlying currencies.

Once you have calculated the present value of the future cash flows, you need to add them together to get the value of the CCS. The value of the CCS will be positive if the present value of the cash flows in the first currency is greater than the present value of the cash flows in the second currency. The value will be negative if the opposite is true.

Here is an example of how to value a CCS:

Party A is exposed to a risk of a depreciation of the euro against the dollar.
Party B is looking to take advantage of a depreciation of the euro against the dollar.
The notional amount of the CCS is $10 million.
The swap is for a period of 1 year.
The current exchange rate is $1 = €1.
The risk-free interest rate in the United States is 5%.
The risk-free interest rate in the eurozone is 4%.

The present value of the future cash flows in the United States is:

$10 million * 1.05 = $10.5 million

The present value of the future cash flows in the eurozone is:

€10 million * 1.04 = €10.4 million

The value of the CCS is:

$10.5 million - €10.4 million = $0.1 million

Therefore, the CCS is worth $0.1 million. This means that Party A would pay Party B $0.1 million in exchange for the CCS.

It is important to note that the value of a CCS can change over time as the exchange rate fluctuates. If the euro depreciates against the dollar, the value of the CCS will increase. If the euro appreciates against the dollar, the value of the CCS will decrease.