Introduction

Currency swaps are complex financial instruments that allow parties to exchange cash flows denominated in different currencies. Valuing currency swaps accurately is crucial for assessing their potential benefits and risks. One common approach to valuing currency swaps involves utilizing a sequence of forward exchange rates. This chapter delves into the methodology of calculating the value of a currency swap based on forward exchange rates, providing insights into the mechanics of the process along with practical examples.

Valuation Methodology

Calculating the value of a currency swap using a sequence of forward exchange rates involves two primary steps: determining the present value of each cash flow and aggregating these present values to derive the total value of the swap.

1) Determining Present Value of Cash Flows For each leg of the currency swap, the future cash flows are estimated based on the agreed-upon notional amounts, interest rates, and exchange rates. These cash flows are then discounted to their present value using the appropriate forward exchange rates using below formula:

$$PV=\frac{CF}{(1+r)^n}$$

Where:

• $PV$: Present Value
• $CF$: Future Cash Flow
• $r$: Applicable Discount Rate (derived from forward exchange rate)
• $n$: Number of Periods

2) Aggregating Present Values
Once the present value of each cash flow is determined, the values from both legs of the swap are aggregated to calculate the overall value of the currency swap using below formula:

$$\text{Currency Swap Value = PV(Leg 1 Cash Flows) - PV(Leg 2 Cash Flows)}$$

Example: Consider a currency swap between Company A and Company B. Company A agrees to pay fixed-rate USD and receive fixed-rate EUR, while Company B agrees to pay fixed-rate EUR and receive fixed-rate USD. The notional amount is USD 1 million, and the swap has a tenor of 5 years. Forward exchange rates for each year are as follows:

• Year 1: USD/EUR = 0.90
• Year 2: USD/EUR = 0.85
• Year 3: USD/EUR = 0.80
• Year 4: USD/EUR = 0.75
• Year 5: USD/EUR = 0.70

Given that the fixed rate for USD is 4% and the fixed rate for EUR is 3.5%, the valuation can be calculated step by step for each year.