FX Swap Valuation
A foreign exchange swap or currency swap is a contract under which two parties agree to exchange two currencies at a set rate and then to re-exchange those currencies at an agreed upon rate at a fixed date in the future. Therefore, an FX swap consists of two transactions: a spot transaction and a forward transaction.
An FX swap or currency swap agreement is a contract in which both parties agree to exchange one currency for another currency at a spot FX rate. The agreement also stipulates to re-exchange the same amounts at a certain future date also at a forward FX rate. Many people confuse currency swaps with cross currency swaps. They are totally different. A cross currency swap is an interest rate swap in which two parties to exchange interest payments and principal on loans denominated in two different currencies.
In a currency swap, one party simultaneously borrows one currency and lends another currency to a second party. The repayment obligation is used as collateral and the amount of repayment is fixed at the FX forward rate. FX swaps can be considered riskless collateralized borrowing/lending. The contract virtually allows you to utilize the funds you have in one currency to fund obligations denominated in a different currency, without incurring foreign exchange risk.
A currency swap is a simultaneous purchase and sale of identical amounts of one currency for another with two different value dates, normally spot to forward. Therefore, an FX swap consists of two transactions: a spot transaction and a forward transaction. Effectively the FX swap is two exchange contracts packed in one: a spot foreign exchange transaction and a forward foreign exchange transaction.
A currency swap deal can be used if you have a currency, which you do not need before a certain time, but at the same time have a short-term need for another currency. Swap deals are used for managing currency risks, postponing the term of forward-deal and optimizing financing.
The most common use of FX Swaps is for institutions to fund their foreign exchange balances. FX swaps are also used by importers and exporters, as well as institutional investors who wish to hedge their positions. They are also used to speculate and, by incurring a risk, attempt to profit from rising or falling exchange rates.
Currency swaps are OTC trades and have credit risk. In the case that one of the parties is unable to fulfill its obligation, the other party will have to sign another contract with a third party, thus being exposed to market risk at that time. This presentation gives an overview of FX swaps and valuation model.
Given spot rate X_s , spot date T_s and forward date T, the FX forward rate can be represented as
{(X_f=X_s (D_b (T_s,T))/(D_q (T_s,T)) if T≥T_s@X_f=X_s (D_q (T,T_s))/(D_b (T,T_s)) if T<T_s )┤ where X_s the spot FX rate quoted as base/quote t the valuation date T_s the spot date (several days after the valuation date) T the forward date D_b (T_s,T) the discount factor of base currency from spot date to forward date D_q (T_s,T) the discount factor of quote currency from spot date to forward date
An FX swap is a simultaneous purchase and sale of identical amounts of one currency for another with two different value dates, normally spot date and forward date. Therefore, an FX swap has two legs – a spot transaction and a forward transaction.
In the spot leg, a particular quantity of a currency is bought or sold versus another currency at an agreed upon rate on the spot date. In the forward leg, the same quantity of currency is then simultaneously sold or bought versus the other currency at a second agreed upon rate on the forward date.
From valuation perspective, an FX swap can be viewed as a combination of two forward contracts. In general, it has a long FX forward contract and a short one. Typically, one leg of the outstanding contract would have already expired. Therefore, in many situations, an FX swap is equivalent to an FX forward contract.
The present value of an FX forward contract is given by
PV(t)=N_b D_b (t,T) X_0-N_q D_q (t,T) where t the valuation date T the payment date X_s the spot FX rate quoted base/quote D_b (t,T) the discount factor of base currency from valuation date to forward date D_q (t,T) the discount factor of quote currency from valuation date to forward date N_b the notional principal amount for base currency N_q the notional principal amount for quote currency
References: