FBE459_1_2a_Futures_Pricing

# FBE459_1_2a_Futures_Pricing - Lecture 1.2 Outline FBE 459...

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1 FBE 459 – Financial Derivatives Prof. Pedro Matos Lecture 1.2(a): Futures Pricing and Hedging (Part A) Determination of forward price • Determination of forward price Readings: HULL chapters 3, 5 - 1.2.(a): Determining Forward Prices (*today*) . Arbitrage Pricing - 1.2.(b): Hedging Convergence and Basis Risk Lecture 1.2 Outline: 2 . Convergence and Basis Risk . Contango and Backwardation . Hedging and Cross-Hedging Forward Price Forward contract : buyer and seller agree upon the delivery of a specified quantity and quality of an asset at a future date for a given price. Contract agreed today (t=0)… For future date (t=T)… 3 ? Terms and conditions: - Price (F 0 ) - Quantity & Quality of asset - Settlement date (T) - Location for delivery On settlement: - Delivery of asset - Payment of F 0 Forward Price How is F determined? -> How much to pay for asset (oil, gold, OJ,…) today? => answer: 4 -> How much to pay for asset (oil, gold, OJ,…) in future (6m)? => answer:

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2 Forward Price How is F determined? by Arbitrage Pricing What would it cost to buy the asset today, hold it to the future date and just deliver it? F 0 = FV (S 0 ) 5 FV (S S 0 = spot price of the underlying asset (today) F 0 = future price (set today) FV means calculating future value at maturity [ similarly, S 0 = PV (F 0 ) where PV means discounting from maturity to today] Forward Price How is F 0 determined? by Arbitrage Pricing … think about the seller, how can he deliver the asset at t=T? today (t=0) at maturity (t=T) .forward 6 . forward contract . how can the Seller “hedge”? Buyer Buyer Buyer Buyer Sel er Sel er Sel er Sel er Forward Price today (t=0) at maturity (t=T) . Short the futures . Settle futures: deliver gold in exchange for F 0 … so borrowing to buy asset today replicates a short position in forward, and writing down the cash-flows: 7 . Buy Asset . Borrow . Asset . Pay back the loan Profit [at t=0]= Profit [at t=T] = => arbitrage: absence of any riskless profits, so how do we make zero profit at t=0 and t=T? F 0 = Forward Price Example 1: Gold futures Suppose that: . The spot price of gold is S 0 = US\$390 . The 1-year US\$ interest rate is r = 5% per annum No income or storage costs for gold 8 . In our example, S 0 = , T = , and r = so that F 0 =
3 Forward Price Example 1 (Cont.): What if the quoted 1-year forward price of gold is F 0 = US\$425. What is the arbitrage opportunity? Arbitrage strategy “buy low sell high” 9 Arbitrage strategy buy low, sell high . “buy low” (what is cheap?) : ………………………… . “sell high” (what is expensive?) : …………………… -> go long on ………… , go short on …………

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FBE459_1_2a_Futures_Pricing - Lecture 1.2 Outline FBE 459...

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