Currency Swaps (Lecture notes)

A currency swap (also called cross currency interest rate swap) is a contract that involves exchanging principal and interest payments on a loan on one currency for principal and interest payments on an approximately equivalent loan in a different currency. Each loan can have a fixed or floating rate.

The rationale for the swap is that each party has a comparative advantage in one of the currencies’ credit market due, for example, to reputation, brand recognition, trust.

The reason for the deal is that the two parties involved need to borrow in the other currency.

Example: A German company offers a US company a €40 loan at a fixed rate of 6% in return for a $36m loan at a fixed rate of 8%. The exchange rate is currently $0.9/€

Valuation Method 1 – Fixed Bonds

A currency swap can be decomposed into two risk-free bonds. If the foreign currency is received and domestic currency is paid, its value to company A

is

V = SB* - B = 0

The value is calculated in this way because we are looking from the perspective of the German company.

Coupon (Ger) = 6% x 40 = 2.4Coupon (US) = 8% x 36 = 2.88The US $ is the domestic currency.

S = exchange rate in direct quotation (domestic currency/1 unit of foreign currency)B* = present value of foreign denominated bond in foreign currencyB = present value of the domestic currency bond

Note that the value of the contract is zero at t=0.

Principal (coupon + face value)

Face value = PV of loans

Valuation Method 2 – Forward Contracts

A currency swap can be decomposed in a series of forward contracts for each interest payment exchange:

(Pmt* x Ft – Pmt)*(1 – r)-t

and the value of the exchange of principals at tn is

(B*FT – B)*(1 + r)-T

When the contract starts, the sum of the above discounted values is zero (assuming that the covered interest parity holds).

Spot rate

r

r*

Present value of loans

During the life of the currency swap, its value is a function of the term structure of the forward rates and the term structure of the domestic interest rates.

where:

Pmt*, Pmt: fixed interest payment in FC and DC respectively

Ft: forward exchange rate at time t

r: domestic interest rate

B*= value of foreign denominated bond in FC

B = value of the domestic currency bond

0.9 x (1.08/1.06) = 0.9169…

Types of risk intrinsic in currency swaps:

Price risk (due to interest rate risk, exchange rate risk). Credit risk (especially for swap intermediaries). Mismatch risk. Sovereign risk (exchange rate/capital control restrictions).