Introduction

In the world of financial derivatives, currency swaps play a pivotal role in managing currency risk and achieving financial goals. One approach to valuing currency swaps involves considering two simultaneous bond positions. By understanding the interplay between these positions and the inherent exchange of cash flows, one can effectively determine the value of a currency swap. This chapter delves into the mechanics of this valuation method, providing insights into how two bond positions interact within the context of a currency swap.

Valuing Currency Swap using Two Bond Positions

Valuing a currency swap using two simultaneous bond positions relies on the idea that the currency swap can be broken down into two separate synthetic positions – one in the domestic currency and another in the foreign currency. These synthetic positions mirror the cash flows of the currency swap, and their combined value reflects the overall value of the currency swap.

Step 1: Creating Synthetic Bond Positions

• Identify the cash flows exchanged in the currency swap – fixed interest payments in one currency for variable interest payments in another currency.
• Create a synthetic position in the domestic currency using a fixed-rate bond that matches the fixed interest payments of the currency swap.
• Construct a synthetic position in the foreign currency using a floating-rate bond that mirrors the variable interest payments of the currency swap.

Step 2: Calculating Bond Position Values

• Determine the present value of future fixed interest payments of the domestic synthetic bond using the fixed rate and the time to each payment.
• Calculate the present value of anticipated floating-rate payments of the foreign synthetic bond, considering the expected future interest rates and the time to each payment.

Step 3: Aggregating Synthetic Positions

• Sum the present values of the fixed and floating interest payments to derive the total value of the synthetic positions.

Step 4: Determining Currency Swap Value

• The value of the currency swap is the difference between the total value of the synthetic positions in the domestic and foreign currencies.

Example: Suppose a currency swap involves exchanging fixed payments of 5% in US dollars for variable payments based on the London Interbank Offered Rate (LIBOR) in euros. Consider a synthetic fixed-rate bond in US dollars and a synthetic floating-rate bond in euros, both with a notional value of USD 1 million and 1 million euros respectively.

• The present value of fixed payments in dollars, assuming a 5% fixed rate and three years remaining until maturity, amounts to USD 150,000.
• The present value of anticipated floating-rate payments in euros, considering projected LIBOR rates, equates to 100,000 euros. The total value of the synthetic positions would be 150,000+100,000 = 250,000 euros.

Hence, the value of the currency swap based on these simultaneous bond positions would be USD 250,000.