Derivatives09-8 - Forward and Futures Contracts

Derivatives09-8 - Forward and Futures Contracts -...

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Derivatives Session 9. Forward and Futures Contracts
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Where we are Last Session: Introduced some general ideas & concepts in Options, Futures and Derivatives (Chapter 1, OFOD) This Session: Focus on fundamentals of Forward and Futures Contracts (Chapters 2-3, OFOD) Next Session: Interest Rates and the Value of Future Cash (Chapter 4, OFOD)
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Plan for This Session Situation of the Japanese Bank Arbitrage in the forward market for gold Fundamental Cash & Carry no arbitrage condition Mechanics of Futures Instruments and Markets Margin Forwards vs. Futures Fundamentals of Futures Hedging Strategies
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Real World Situation - Cash Japanese Bank: Borrow USD in Interbank Euromarket for 3 month term, T Could perform the same transaction as a Synthetic in the FX and domestic yen mkt Borrow yen in local mkt for term T, at L(t0,Y) Sell yen and buy USD in spot FX mkt at e(t0,Y) Finally, the bank buys yen in the forward FX mkt for delivery at t0+T
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Real World Situation - Cash Cash Flows are Additive + + = t0 t0+T Y Yx(1+L(t0,Y)xT) USD Y Yx(1+L(t0,Y)xT) USD USDx(1+L(t0,$)xT) Borrow Y for T at L(t0,Y) Pay back: Yx(1+L(to,Y)xT) Buy USD sell Y at e(t0,Y) Y=e(t0,Y)xUSD Buy Y forward, t0+T delivery in amount so Yx(1+L(t0,Y)xT) = f(t0,T;Y)xUSD1 USD1=USDx(1+L(t0,$)xT) USDx(1+L(t0,$)xT)
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Real World Situation – Cash At t0 Borrowing rates in USD & Yen are known Exchange rate USD & Yen are known Forward market for Yen must preclude riskless arbitrage so, e(t0,Y)xUSD x (1+L(t0,Y)xT) = f(t0,T;Y) x USDx(1+L(t0,$)xT) or, f(t0,T;Y) = e(t0,Y) x [(1+L(t0,Y)xT) / (1+L(t0,$)xT)]
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Money Rates – Close Friday, 1/26/07 / YEN / 1WK .345 1MO .35 2MO .435 3MO .47 4MO .505 5MO .515 6MO .545 9MO .585 1YR .655 / US DOLLAR / 1WK 5.265 1MO 5.275 2MO 5.285 3MO 5.295 4MO 5.295 5MO 5.355 6MO 5.365 9MO 5.385 1YR 5.39
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Spot/Forwards – USD-JPY U S D -J P Y S P O T / F O R W A R D S Source CMPN Composite (NY) Close Time of Bid Ask Bid Rate Ask Rate Time of PRD Fri 1/26 Offset Offset Offset Rate 2 Spot 16:59 121.54 121.54 121.54 121.54 16:59 1 Week 16:59 -11.59 -11.59 121.42 121.42 16:59 1 Month 16:59 -47.80 -47.80 121.06 121.06 16:59 2 Month 16:59 -96.20 -96.20 120.58 120.58 16:59 3 Month 16:59 -140.80 -140.80 120.13 120.13 16:59 4 Month 16:59 -192.90 -192.90 119.61 119.61 16:59 5 Month 16:59 -239.41 -239.41 119.15 119.15 16:59 6 Month 16:59 -287.14 -287.14 118.67 118.67 16:59 9 Month 16:59 -424.05 -424.05 117.30 117.30 16:59 1 Year 16:59 -554.20 -554.20 116.00 116.00 16:59 2 Year 16:59 -1022.37 -1022.37 111.32 111.32 16:59 3 Year 16:59 -1422.50 -1422.50 107.32 107.32 16:59 4 Year 16:59 -1789.00 -1789.00 103.65 103.65 16:59 5 Year 16:59 -2146.00 -2146.00 100.08 100.08 16:59 * All forward offset rates on this screen are direct quotes from banks; see FRD for rates calculated through USD
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1. Gold: An Arbitrage Opportunity? Suppose that: The spot price of gold is US$300 The 1-year forward price of gold is US$340 The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity?
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2. Gold: Another Arbitrage Opportunity? Suppose that: - The spot price of gold is US$300 - The 1-year forward price of gold is US$300 - The 1-year US$ interest rate is 5% per annum Is there an arbitrage opportunity?
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The Forward Price of Gold – The Principal of Cash and Carry If the spot price of gold is S(t0) and the forward price for a contract deliverable in T years is F(t0,T) , then Can borrow money, buy gold, and sell the commodity forward - where there should be no arbitrage: F(t0,T) - S(t0) x (1+ r ) T
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Derivatives09-8 - Forward and Futures Contracts -...

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