Swaps II BS3515 Financial Derivatives PDF

Swaps II BS3515 Financial Derivatives Dr. Dudley Gilder [email protected] Reading: Hull, J. "Options, futures and other derivatives", 11th Global Edition Chapter 7, Sections 7.8, 7.9 Outline...

Swaps II BS3515 Financial Derivatives Dr. Dudley Gilder [email protected] Reading: Hull, J. "Options, futures and other derivatives", 11th Global Edition Chapter 7, Sections 7.8, 7.9 Outline Currency swap Motives for using currency swaps Valuing currency swaps 1 / 17 Definition of Currency Swaps We will look at “plain-vanilla” fixed-for-fixed currency swaps Interest rates are fixed in each currency when the swap is initiated Note, the principal is exchanged at the beginning and end of the life of a currency swap (Remember, in an interest rate swap, the principal is not exchanged) Principal is specified in each currency 2 / 17 Definition of Currency Swaps Example An agreement to pay 5% on a sterling principal of £10,000,000 & receive 6% on a US$ principal of $15,000,000 every year for 5 years 3 / 17 Outline Currency swap Motives for using currency swaps Valuing currency swaps 4 / 17 Motives for using currency swaps Asset transformation: transforming an investment and corresponding cashflows in one currency denomination and the respective interest rate income to another Liability transformation: transforming borrowing and corresponding cashflows from one currency denomination and the respective interest payments to another Comparative advantage: Firms may have a comparative advantage borrowing in a particular currency. Note, unlike with fixed-for-floating interest rate swaps, the comparative advantage may be real because of taxes. 5 / 17 Comparative advantage General electric wants to borrow 20 million AUD Quantas wants to borrow 15 million USD Current exchange rate = 0.75 USD/AUD USD AUD GE 5%* 7.6% Quantas 7% 8%* QSD 2% 0.4% ∆1.6% FI charges 0.2%. How can a swap be designed to benefit each company equally? 6 / 17 Comparative advantage QSD is the total benefit to all parties. After the FI has taken their share, the firms can share: 1.6-0.2=1.4% If shared equally, GE and Quantas will be able to reduce their borrowing costs by: 1.4/2 = 0.7% After entering the swap, the effective borrowing rate to GE will be 7.6-0.7=6.9% in AUD After entering the swap, the effective borrowing rate to Quantas will be: 7-0.7=6.3% in USD 7 / 17 Comparative advantage 6.9%AUD 8% AUD GE FI Quantas 5% USD 6.3% USD 5% USD 8% AUD Bank X Bank Y 8 / 17 Outline Currency swap Motives for using currency swaps Valuing currency swaps 9 / 17 Valuing currency swaps Two methods to value currency swaps: 1 Portfolio of forward contracts 2 Bond portfolio 10 / 17 Valuing currency swaps: Forward contracts A currency swap is a portfolio of foreign exchange forward contracts Valuing a currency swap amounts to calculating the value of each forward in the portfolio Valuation procedure is: 1 Find the forward exchange rates 2 Calculate cash flows assuming unknown exchange rates will equal forward exchange rates 3 Discount swap cash flows at the risk-free rate 11 / 17 Valuing currency swaps: Forward contracts Forward exchange rate can be found as follows: F0 = S0 e (r −q)T = S0 e (r −rforeign )T where r is the domestic risk-free rate, rforeign is the risk-free rate in the foreign currency, T is the time to maturity, S0 is the spot exchange rate, and F0 is the forward exchange rate The foreign currency is the asset underlying the contract and provides a yield (q) equal to the risk-free interest rate in that currency 12 / 17 Valuing currency swaps: Forward contracts Example A US firm (domestic) has entered into a swap where it pays 8% per annum (with annual compounding) in USD on a principal of $10 million and receives 5% per annum (with annual compounding) in Yen on a principal of 1,200 million Yen. The swap has three more years until expiry. The current exchange rate is 110 Yen per US dollar. The zero curves in the US and Japan are flat and the corresponding risk-free rates (with continuous compounding) are 9% and 4%, respectively. 13 / 17 Valuing currency swaps: Forward contracts Example Year $ CF Yen CF Forward Yen CF ($) Net CF ($) PV FX rate 1 -$0.8m ¥60m 0.009557 $0.5734m -$0.2266m -$0.2071m 2 -$0.8m ¥60m 0.010047 $0.6028m -$0.1972m -$0.1647m 3 -$10.8m ¥1,260m 0.010562 $13.3083m $2.5083m $1.9148m Total $1.543m Vswap = $1.543m 14 / 17 Valuing currency swaps: Bond portfolio Assume USD is domestic currency If USD are received and foreign currency paid, then swap value is: Vswap = BD − S0 BF If foreign currency is received and USD are paid, then swap value is: Vswap = S0 BF − BD Where, ▶ BD = value of USD (domestic) bond (measured in, domestic, USD) ▶ BF = value of foreign bond (measured in foreign currency) ▶ S0 = spot exchange rate (USD per unit of foreign currency) 15 / 17 Valuing currency swaps: Forward contracts Example Year $Bond CF ($) PV ($) ¥Bond CF (¥) PV (¥) 1 $0.8m $0.7311m ¥60m ¥57.65m 2 $0.8m $0.6682m ¥60m ¥55.39m 3 $10.8m $8.2445m ¥1,260m ¥1117.52m Total $9.6438m ¥1230.56m $1 Vswap = S0 BF − BD = ¥1230.56m × − $9.6438m = $1.5431m ¥110 16 / 17 Summary Currency swap Motives for using currency swaps Valuing currency swaps 17 / 17