Futures and Options Supplement

Futures and Options Supplement - Future and Options s...

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1 Futures and Options Forward (futures) contracts Forward-spot parity relation Implied riskless return Limitations to arbitrage Calls and puts Put-call parity relation Covered calls, protective puts, synthetic forwards Binomial option pricing Black-Scholes formula
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Fall 2001   A standard forward contract is an agreement in which the buyer agrees to buy from the seller an underlying asset for a fixed price ( delivery price ) during a future period of time ( delivery period ), where the terms are initially set so that its present value is zero. Standard Forward Contracts Definition payoff = S t K with K set initially so that PV 0 (S t K ) = 0 [ K = F 0 ] S 0 current underlying asset price (spot price) S t underlying asset price on delivery date K delivery price of contract t current time-to-delivery of contract (in years) r riskless return (annualized) (1 plus interest rate) d payout return (annualized) (1 plus dividend yield) F 0 current forward price (sets PV 0 (S t F 0 ) = 0 )
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Fall 2001   S 0 = 100 t = 1 r = 1.15 d = 1.00 Future Asset Price ( S t ) 50 75 F 0 = S 0 (r/d) t = 100(1.15/1.00) 1 = 115 Loss Profit Standard Forward Contracts BUY FORWARD (profit/loss diagram)
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Fall 2001   February 13, 1997 buy 1 March S&P 500 Index future @ $814.15 futures price Standard Forward Contracts Example (futures ) March 20, 1997 (Thursday): 3:15 p.m. Central Time secondary market trading ceases March 21, 1997 (Friday): 8:30 a.m. Central Time final change in futures price over the last day is transferred each trading day from February 14, 1997 through March 20, 1997 RECEIVE 250 × increase of futures price into buyer’s account and PAY OUT 250 × decrease in futures price from buyer’s account or close out position by OFFSETTING the future by selling it back or EXCHANGE FOR PHYSICALS (on rare occasions) Some futures, such as S&P 500 Index futures, settle in cash, rather than physical delivery.
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Fall 2001   match trades pass cash payments/commodities between counterparties collect clearing margin guarantee transactions (reduce credit risk) “marking-to-the-market” for futures (reduce credit risk) Buyer Seller Buyer’s Clearing Member Seller’s Clearing Member Clearinghouse Exchange Buyer’s Floor Broker Seller’s Floor Broker Buyer’s Broker Seller’s Broker Clearinghouses (for Futures and Exchange-Traded Options)
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Fall 2001   Assume : no arbitrage competitive markets underlying asset not held for consumption or use in production Current Date Delivery Date Buy Forward Contract 0 S t F 0 Buy one unit of Underlying Asset – 100 S t Borrow PV 0 of Forward Price F 0 /1.15 F 0 Total – 100 + F 0 /1.15 S t F 0 – 100 + F 0 /1.15 = 0 F 0 = 115 S 0 = 100 t = 1 r = 1.15 d = 1.00 Forward-Spot Parity Relation Numerical Example ( F 0 /1.15 ) × 1.15 = F 0
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Fall 2001   S 0 = 100 t = 1 r = 1.15 d = 1.00 Future Asset Price ( S t ) 50 75 Borrowing Buy Asset Loss Profit Forward-Spot Parity Relation Synthetic Forward: ASSET + BORROWING Forward Contract Value at Inception = $100 – ($115/1.15) 1 = $0 Synthetic Forward
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Fall 2001   Forward-Spot Parity Relation Arbitrage Table Current Date Delivery Date Buy Forward Contract 0 S t F 0 Buy d –t units of Underlying Asset – S 0 d –t (S t
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This note was uploaded on 02/21/2010 for the course FINA 221 taught by Professor Na during the Spring '09 term at HKUST.

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Futures and Options Supplement - Future and Options s...

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