1. © K. Cuthbertson and D. Nitzsche Figures for Chapter 2 FUTURES MARKETS (Financial Engineering : Derivatives and Risk Management)

2. © K. Cuthbertson and D. Nitzsche Figure 2.1 : Types of derivative markets OVER-THE-COUNTER Supplied by intermediaries (banks) Customised to suit buyer Can be done for any amount, any settlement date Credit risk of counterparty and expensive to unwind Allows anonymity - important for large deals New contracts do not need approval of regulator EXCHANGE TRADED Traded on exchanges (e.g. LIFFE, CBOT, CME) Available for restricted set of assets Fixed contract sizes and settlement dates Easy to reverse the position Credit risk eliminated by clearing house margining system (‘marking to market’)

3. © K. Cuthbertson and D. Nitzsche Figure 2.2 : Financial futures markets INSTRUMENTS Money Market Instruments 3 month Eurodollar deposit, 90 day US T-bills, 3 month Sterling or Euro deposits Bonds US T-bond, German Bund Stock Indices S&P500, FTSE100 Currencies Euro, Sterling, Yen, etc. Mortgage Pools (GNMA) EXCHANGES CBOT CME NY Futures Exchange Philadelphia Exchange (PHLX) Pacific Stock Exchange (PSE) LIFFE (London) MATIF (Paris) Eurex (Frankfurt) Singapore (SIMEX), Hong Kong, Tokyo, Osaka Sydney Futures Exchange (SFE)

4. © K. Cuthbertson and D. Nitzsche Figure 2.3 : Speculation with futures Futures price Profit per contract $10 -$10 0 Long future Short future F 2 = 110 F 2 = 90 F 1 = 100

5. © K. Cuthbertson and D. Nitzsche Figure 2.4 : Profit payoff (direction vectors) Long Futures or Long Spot 100 110 10 +1 Profit +1 Short Futures or Short Spot 100 90 10 Profit

6. © K. Cuthbertson and D. Nitzsche Figure 2.6 : Arbitrage with futures Stock price S = $100 Safe rate r = 4% p.a. Quoted futures price F = $102 Strategy today Sell futures contract at $102 (receive nothing today) Borrow $100, but stock (= synthetic future) Use no ‘own funds’ 3 months time (T = 1/4) Loan outstanding = $100 (1+0.04/4) = $101 Deliver stocks and receipts from F.C. = $102 Riskless profit = $1

7. © K. Cuthbertson and D. Nitzsche Figure 2.7 : Backwardation and Contango Stock price, S t For simplicity we assume that the spot price remains constant. In practise, S and hence F will fluctuate as you approach T but with F t > S t if the market is in contango and F t < S t if the market is in backwardation. T Forward price in contango : F > S Forward price in backwardation : F < S 0 At T, S T = F T

8. © K. Cuthbertson and D. Nitzsche Figure 2.8 : Hedging using futures = 0 - 1 + 1 Long Underlying + Short Futures = Hedge

9. © K. Cuthbertson and D. Nitzsche Figure 2.9 : Rolling over a futures contract AprilJuneOct.Dec.AprilJuneSept. Short Sept. Future Close out Sept. Future Buy March Future Close out March Future Buy Sept. Future Close out Sept. Future March AugustFebruaryAugust

10. © K. Cuthbertson and D. Nitzsche Figure 2.10 : Value of forward contract JanuaryMarchJune Initial 6-month forward F 0 = K = $90 Value of initial 6-month forward V t = (F t - F 0 ) e -r(T-t) New 3-month forward F t = $101.25 Both forward contracts expire