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Lecture2_PricingForwardsFutures_I

# Lecture2_PricingForwardsFutures_I - NBA 6730 Derivative...

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1 NBA 6730: Derivative Securities Lecture 2: Pricing Forwards and Futures I 08/31/2010 George Gao NBA6730-Derivative Securities I 2 Agenda This lecture answers a central question about forwards and futures pricing: How is the forwards and futures price set relative to the current spot price? Cost of carry model: pricing commodity forwards Replicating portfolio: pricing stock futures

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2 NBA6730-Derivative Securities I 3 (1) Oil Example Given numbers: crude oil = \$70/barrel (spot price) storage cost = \$2/barrel (payable ex-post) 1-year interest rate = 5% (annual compound) Question: what is the 1-year forward price for oil? First, we see an equilibrium argument by starting with two scenarios and describing the net cash flow under each case. Then, we see an arbitrage argument . Case 1: you OWN 100 barrels of oil Case 2: you NEED 100 barrels of oil NBA6730-Derivative Securities I 4 (1) Oil Example: You Own 100 Barrels of Oil Choice 1: sell the oil and put the money into a bank (cash flow out in red) Choice 2: store the oil and sell in the future. If require the same CFs as above, what’s the forward price? t=0 t=1 Sell the oil now \$7,000 - Earn 5% from the bank (\$7,000) \$7,000*(1+5%)=\$7,350 Net cash flow (CF): 0 \$7,350 t=0 t=1 Hold & store the oil 0 (\$200) Sell in the future - ?? Net cash flow (CF): 0 \$7,350
3 NBA6730-Derivative Securities I 5 (1) Oil Example: You Need 100 Barrels of Oil Choice 1: borrow from a bank, buy and store the oil, return the loan in the future Choice 2: do nothing now and buy in the future. If you’re indifferent between these two choices…… t=0 t=1 Borrow \$7K from a bank \$7,000 - Buy 100 barrels of oil (\$7,000) - Store the oil - (\$200) Pay back the loan - (\$7,350=7k*[1+5%]) Net cash flow (CF): 0 (\$7,550) t=0 t=1 Net cash flow (CF): 0 (??) NBA6730-Derivative Securities I 6 (1) Oil Example: Forward Price No matter whether you own or need 100 barrels of oil, IF you are indifferent between choices 1 and 2, the forward price (at either buy or sell) equals: \$ ଻,଴଴଴ൈ ଵାହ% ାଶ଴଴ ଵ଴଴ ൌ \$75.50/barrel But why MUST you be indifferent between those two choices (i.e., in equilibrium)? No-arbitrage principle and law of one price If the forward price is not equal to \$75.50, then there will be an arbitrage opportunity

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