Financial Instruments: Derivatives KPMG. All rights reserved. 1

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2 1. Introduction Financial Risk Management data technology strategy Risk tolerance operations Management Infrastructure autorisation people M.I.S. methods disclosure RARORAC VatR Valuation Operational risk Market risk credit 2003 KPMG. All rights reserved. 2

7 I.R.S.-Pricing Galactic Industries (GI) wishes to enter into a swap in which GI will pay cash flows based on a floating rate and receive cash flows based on a fixed rate. In the jargon of the swap market, Galactic-the floating-rate payer- is referred to as the seller of the swap (or as short the swap). Market convention is to quote the terms of interest rate swaps as the floating-rate index (normally LIBOR) flat against some fixed rate; GI will pay cash flows based on the floating rate flat and will receive cash flows based on a fixed rate of X percent. The question is What is the appropriate fixed rate; what is X? To keep calculations at a minimum, suppose GI requested a quote from the BANCORP (BC) on the following simple swap: National principal amount : $100 Maturity 1 year Floating index 6-month LIBOR Fixed coupon?% Payment frequency semi-annual Day count 30/360 From these terms, we know what GI will pay: at the 6-month settlement, GI pays a coupon determined by the 6-month LIBOR rate in effect at contract origination. At the 12 month settlement GI s coupon payment is determined by the 6-month LIBOR prevailing at month 6. What is missing is the fixed interest rate that will determine the payments GI will receive from BC KPMG. All rights reserved. 7

8 I.R.S.-Pricing Suppose that the Libor yield curve-the spot yield curve-prevailing at origination of this swap is the simplified yield curve shown below: 10% 8% Questions 6 month 1 year Time to maturity II.1 Please calculate the fixed coupon rate on a yearly basis. II.2 If the 6-month Libor increases to 9% and the 1 year Libor to 11% (keep all other variables at the same level); calculate the market value of this swap for the Bancorp KPMG. All rights reserved. 8

9 Forward Rate Agreement (FRA) 3 m 6 m c= notional amount i m = reference rate i g = guaranteed rate n 1 = 3m n 2 = 6m i m > i g : seller pays buyer i m < i g : buyer pays seller 2003 KPMG. All rights reserved. 9

11 FRA The company ROTTA S.A. has contracted a loan of EURO (Floating Rate Note interest rate = 3-month Euribor + ¾%). The Management of ROTTA wants to hedge the risk related to a rise in interest rates, and buys/sells for this reason a 3 against 6 FRA contract. The counterpart of this transaction is the bank Martin Transav N.V. This bank agrees to buy/sell the FRA contract against a guaranteed rate of 9%. Question A: Does ROTTA have to buy or to sell the FRA contract in order to hedge the interest rate risk related to its loan? Scenario I: The EURIBOR after three months amounts to 8%. Question B. How much does the company pay/receive to/from the bank in scenario I, expressed in a yearly interest rate percentage? Question C: What are the interest charges of the loan for the three coming months in scenario I, expressed in a yearly interest rate percentage? 2003 KPMG. All rights reserved. 11

12 FRA Question D: What are the charges to be paid by the company for the three coming months (loan/fra position) in scenario I, expressed in an interest rate percentage? Scenario II: The EURIBOR after three months amounts to 10% Question E: How much does the company have to pay/receive to/from the bank in scenario II, expressed in an interest rate percentage? Question F: What interest rate does the company have to pay for the following three months according to scenario II? Question G: What charges does the company have to pay for the three coming months (loan + FRA position) following scenario II, expressed in an interest rate percentage? 2003 KPMG. All rights reserved. 12

14 Option Premium Intrinsic value Call: exercise price < spot rate Put: exercise price > spot rate If intrinsic value > 0: in the money If intrinsic value = 0: at the money If intrinsic value < 0: out of the money Time and expectation value - exercise price - Time to maturity - Volatility - Interest rate 2003 KPMG. All rights reserved. 14

15 Option Valuation Basic model Black & Scholes c = kn (d 1 ) e -rt U N (d 2 ) ln( k / U ) + rt d 1 = +1/2 σ T σ T d 2 = d 1 σ T k U r T N = spot rate = exercise price = risk free interest rate = time to maturity = standard deviation = standard normal distribution N(d1) = (pseudo)-probability call in the money at expiry date 2003 KPMG. All rights reserved. 15

17 Put Call parity Investment transaction Cash inflow now Cash flow at option Maturity date Write call c k*<=u 0 k*>u U-k* Buy put -p U-k* 0 Buy underlying asset -k k* k* Borrow B T U -U -U c-p-k+ B T U 0 0 HAD TO BE 0 c= p+k- B T U 2003 KPMG. All rights reserved. 17

18 CAP Cap writer Cap premium Cap agreement At the end of each payment period Cap buyer Cap writer 1) No payments if 3-month EURIBOR < =12% Cap buyer Cap writer 2) Payments if 3-month EURIBOR > 12% (1/4) x (3-month EURIBOR-12%) x (nominal amount) Cap buyer 2003 KPMG. All rights reserved. 18

19 Floor writer FLOOR Floor premium Floor agreement At the end of each payment period Floor buyer Floor writer 1) If 6-month EURIBOR >= 8% no payments Floor buyer Floor writer 2) If 6-month EURIBOR <8% (1/2) * (8% - 6month EURIBOR) *(nominal amount) Floor buyer 2003 KPMG. All rights reserved. 19

20 Collar buyer (cap buyer) (floor writer) Collar buyer COLLAR Cap premium Floor premium At the end of each payment period 1) If 7% <=6-month EURIBOR <=11% no payments Collar writer (floor buyer) (cap writer) Collar writer Collar buyer 2) If 6-month EURIBOR <7% (1/2) * (7% - 6-month EURIBOR) *(nominal amount) Collar writer Collar buyer 3) If 6-month EURIBOR > 11% (1/2) * (6-month EURIBOR 11%)*(nominal amount) Collar writer 2003 KPMG. All rights reserved. 20

21 To hedge or Not to hedge Edwin Charles, the treasurer of Benzoe Corp., plans to take down a $10 million loan within the next quarter. The loan rate will be set at the time of the takedown, at three-month LIBOR plus 100 basis points. This rate will be reset each quarter on balances remaining outstanding. Clearly, if interest rates rise before the takedown, Benzoe s interest expenses will rise commensurately, but if rates fall, lower interest expenses will result. How can Edwin protect: himself against the unknown at the lowest possible cost? Strategy 1: Do nothing. This choice would be most appropriate if Edwin thinks that the likelihood that interest rates will rise is limited or negligible. He, of course, must be comfortable living with the consequences if his assessment turns out to be wrong. Strategy 2: Lock in an interest rate today. This may be accomplished by selling Eurodollar futures contracts timed to expire at about the same time as the loan rate is to be set. Any expiration mismatch will foster some uncertainty or basis risk, but less risk than the prevailing market interest rate exposure itself. The rate that Edwin can secure would be 100 basis points above the rate implied by the futures contract (that is, 100 minus the futures price). The additional 100 basis points reflect the bank s spread over LIBOR. Suppose that today 3-month LIBOR is at 7% and that the Eurodollar futures contract is at 92,90 (in other words at a rate of 7.10%) 2003 KPMG. All rights reserved. 21

22 To hedge or Not to hedge Strategy 3: Insure against rising rates. Bying an interest rate cap or buying puts on Eurodollar futures will accomplish this end. Doing either involves an initial cash outlay, which will vary depending on the level of the cap rate (or strike price), the length of time for which the insurance is required, and the market s collective assessment of prospective volatility. But ultimately, if the market rate for LIBOR is higher than the cap rate (or the futures price is lower than the strike price of the put option), the final value of the cap will compensate for the market rate being higher than the ceiling rate. This strategy may sound like the most attractive one-until Edwin goes to write the check for the desired protection. Suppose that the price of a put option on Eurodollar futures with a strike price of (7%) is Before the takedown, it is uncertain which strategy will generate the lower cost of funds. Each alternative hedge strategy should be assessed in light of its cost versus its potential benefits or consequences. Make a table of these benefits and consequences under two scenarios, one in which three-month LIBOR rises to 8% and the other in which three-month LIBOR falls to 6% KPMG. All rights reserved. 22

28 FX Options: Garman Kohlhagen (Elaboration Black & Scholes for currency options) c = e -r o T S N (d 1 ) - e -r c T U N (d 2 ) With d 1 = ln( S / U ) + ( r c r σ T o + 2 0,5σ ) T d 2 = d 1 σ T S= spot rate U= exercise price r o = interest rate option currency r c = interest rate contract currency N(d 1 ) = standard normal figure d 1 N(d 2 ) = standard normal figure d KPMG. All rights reserved. 28

29 FX Options: Range forward Effective purchase price 1,0000 0,9800 0,9700 0,9620 0,9600 0,9550 Forward rate 0,9400 0,9200 0,9200 0,9400 0,9550 0,9600 0,9700 0,9800 1,0000 Spot rate 2003 KPMG. All rights reserved. 29

31 Currency Swap: Initial exchange of the principal 100 million 100 million German subsidiary US$ 100 million A Inc. B GmbH Amercian subsidiary US$ 100 million US$ 100 million 100 million US$ Domestic Bond holders Eurobond holders 2003 KPMG. All rights reserved. 31

32 Currency Swap: Regular exchange of interest 6 million 6 million German subsidiary US$ 7.5 million A Inc. B GmbH Amercian subsidiary US$ 7.5 million US$ 7.5 million 6 million US$ Domestic Bond holders Eurobond holders 2003 KPMG. All rights reserved. 32

33 Currency Swap: Exchange of repayment amounts 100 million 100 million German subsidiary US$ 100 million A Inc. B GmbH Amercian subsidiary US$ 100 million US$ 100 million 100 million US$ Domestic Bond holders Eurobond holders 2003 KPMG. All rights reserved. 33

Financial Instruments: Derivatives

Financial Instruments: Derivatives KPMG. All rights reserved. 1 1. Introduction Financial Risk Management data technology strategy Risk tolerance operations Management Infrastructure autorisation people