6sl - THE UNIVERSITY OF HONG KONG FACULTY OF BUSINESS AND...

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1 T HE U NIVERSITY OF H ONG K ONG F ACULTY OF B USINESS AND E CONOMICS FINA0301 - D ERIVATIVES Second Semester, 2008-2009 Tutorial 4 Slide Chapter 5 & 6 – Financial Forwards and Futures Chapter 7 – Interest Rate Forwards and Futures checkbld Chapter 5 & 6 Proof of Forward Pricing Formula - Stock pays dividend of δ square4 Cash and Carry: F 0 ,T > S 0 × e (r- δ )T Market Maker: Short Forward+ Long Synthetic Forward to reduce risk: (i) Buy Tailed position in stock paying S 0 e - δ T (ii) Borrow S 0 e - δ T If F 0 ,T >S 0 × e (r- δ )T Arbitrage Opportunity Exists
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FINA0301 – Tutorial 4 Slide Mr. Clive Man Chung HO 2 square4 Reverse Cash and Carry: F 0 ,T <S 0 × e (r- δ )T Market Maker: Long Forward Position + Short Synthetic forward to Reduce risk: (i) Short Tailed position in stock receiving S 0 e - δ T (ii) Lend S 0 e - δ T If F 0 ,T <S 0 × e (r- δ )T Arbitrage Opportunity Exists Proof: F 0 ,T = S 0 × e (r- δ )T
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FINA0301 – Tutorial 4 Slide Mr. Clive Man Chung HO 3 Proof of Forward Pricing Formula (with Transaction Cost k ) Bid-ask spreads: S b <S a Transaction cost k : trading forward and stock Interest rate for borrowing and lending: r b >r l No dividends and no Time T transaction cost square4 Cash and Carry: F 0 ,T > S 0 × e (r- δ )T Market Maker: Short Forward Position + Long Synthetic forward to Reduce risk: (i) Buy Tailed position in stock paying S a +k (ii) Borrow S a +2k Time 0 Time T Buy Tailed position -(S a +k) S T in stock Borrow S a +2k S a +2k -(S a +2k)e rbT Short Forward -k F 0 ,T - S T F 0 ,T -(S a +2k)e rbT Arbitrage if F 0 ,T >F + =(S a +2k)e rbT
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FINA0301 – Tutorial 4 Slide Mr. Clive Man Chung HO 4 square4 Reverse Cash and Carry
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