Arbitrage Analysis of Futures Market with Frictions

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1 : (2007) , (, ) : Vignola2Dale (1980) Kawaller2Koch(1984) (cost of carry),.,, ;,, : ;,;,. : ;;; : F83019 : A Arbitrage Analysis of Futures Market with Frictions LIU Hai2long, ZHOU Quan2yi ( Financial Engineering Research Center, School of Management, Shanghai Jiaotong University, Shanghai, ,China) Abstract : Based on Vignola and Kawallerscost of carry model, this paper considers an arbitrage analysis method of Cu futures with frictions caused by transaction costs, storage fees, deliver costs, capital gain taxes and margin. First ex ante and ex post non2arbitrage interval models are proposed for Cu futures, which are then used in case studies. Empirical results show : 1) the ex ante non2arbitrage model is of important sense ; 2) investors have different arbitrage opportunities with different extent due to their difference in costs of capital ; 3) the difference in arbitrage opportunities also results from capital gain taxes. Key words : Cu futures market ; margin ; capital gain taxes ; cost of carry 0., :1984 Kawaller Koch 1980 Vignola2Dale (cost of carry, COC),, COC, [1 ] ; Chow Brophy 1982 Hegde Branch 1985,,, [2,3 ] ;,Poskitt [4,5 ],Chow2Brophy Hegde2Branch,,,Poskitt, ( Implied forward rate, IFR) NZFOE(New Zealand Future and Options Exchange), 2002, IFR,, Barberis Thaler,,, [6 ]. [ 7 ]2 : : ( ) :( ),( ),, ;,.

2 ,2 6 ; [8 ],,,,,,.,,,,,,,,,,,.,,. 1 : 1), ; 2),; 3),; 4) ; 5)., : u ; F k ( t i ) k t i, t i = k - i ( i = 0,1,, k), k t 0 ; S 0 ( ) t 0 ; S k t k ; r. ; 1 ; 2 6 ; 3,; v ; ;. 2,,,,;.,, ( t 0 = k), r : (1 + ) S 0 + (+ ) F k ( t 0 ), (1), ( t k = 0), : - ku + F k ( t 0 ) + F k ( t 0 ) - v ( F k ( t 0 ) - S 0 ), (2) - ku, - v, F k ( t 0 ),F k ( t 0 ), ( F k ( t 0 ) - S 0 ), F k ( t 0 ) S 0,. : (1 + ) S 0 e t 0 r + (+ ) F k ( t 0 ) e t 0 r. (3)

3 , 0,: F k ( t 0 ) ku + v + (1 + ) S 0 e t 0 r + F k ( t 0 ) ( e t 0 r - 1) + F k ( t 0 ) e t 0 r ( F k ( t 0 ) - S 0 ). (4),, 2. 1 () ( t 0 ) ( t k ) (1 + ) S 0 - (1 + ) S 0 e t 0 r (+ ) F k ( t 0 ) - (+ ) F k e t 0 r - (1 + ) S 0 - ku ( F k ( t 0 ) - S 0 ) - (+ ) F k ( t 0 ) F k ( t 0 ) +F k ( t 0 ) - v () ( t 0 ) ( t k ) S (+ ) F k ( t 0 ) - F k ( t 0 ) +F k ( t 0 ) - v (+ ) F k ( t 0 ) - (+ ) F k ( t 0 ) e t 0 r 1 + S S 0 e t 0 r 0,: F k ( t 0 ) - v S 0 e t 0 r - F k ( t 0 ) ( e t 0 r - 1) - F k ( t 0 ) e t 0 r, (5) (0 1).,.,,.,. (4) (5), k ( t 0 = k) - v S 0 e t 0 r ku + v + (1 + ) S 0 e t 0 r - S (+ ) e t 0 r -, 1 +. (6) 1 - (+ ) e t 0 r ,,S 0,F k ( t 0 ),r (1 + ) S 0 + (+ ) F k ( t 0 ),,,, , 0, - (1 + ) S 0, - (+ ) F k ( t 0 ) 3 ( ),3, - ku, - v, F k ( t 0 ), ( F k ( t 0 ) - S 0 ), 1 = 3 F k ( t p ) + [ F k ( t p ) - F k ( t 0 ) ] ( t = t 0 ) ( t = t k ) (1 + ) S 0 - (1 + ) S 0 e rt 0 (+ ) F k ( t 0 ) (1 + ) S ( F k ( t 0 ) - S 0 ) - ku - (+ ) F k ( t 0 ) F k ( t 0 ) v 0 0

4 , - (1 + ) S 0 e rt 0-1, 1 = (+ ) F k ( t 0 ) exp rt 0 + ( 1 F k ( t l ) - F k ( t 0 ) ) exp rt l + ( 2 F k ( t j ) - 1 F k ( t l ) ) exp rt j + ( 3 F k ( t p ) - 2 F k ( t j ) exp rt p + [ F k ( t i ) - i = 1 F k ( t i - 1 ) ]exp rt i, (7) (7), t l t j t p 1 6 ; (+ ) F k ( t 0 ) ; F k ( t i ) - F k ( t i - 1 ) > 0 i F k ( t i ) - F k ( t i - 1 ), ; F k ( t i ) - ( t i - 1 ) < 0 i F k ( t i ) - F k ( t i - 1 ), ; 1 F k ( t l ) - F k ( t 0 ) 1 ; 2 F k ( t j ) - 1 F k ( t l ) 6 ; 3 F k ( t p ) - 2 F k ( t j ).,, 0,:, - ku - v - (1 + ) S 0 e rt 0 - (+ ) F k ( t 0 ) exp rt 0 - ( 1 F k ( t l ) - F k ( t 0 ) ) exp rt l - ( 2 F k ( t j ) - 1 F k ( t l ) ) exp rt j - ( 3 F k ( t p ) - 3 F k ( t p ) + F k ( t p ) - F k ( t 1 ) exp rt 1 + F k ( t 0 ) exp rt 1 - ku + v - F k ( t 0 ) 1 + S 0 + (1 + 2 F k ( t j ) ) exp rt p - ) S 0 e rt 0 + F k ( t 1 ) exp rt 1 - F k ( t p ) + exp rt 1 - (+ ) exp rt 0 + exp rt l - [ F k ( t i ) - F k ( t i - 1 ) ]exp rt i ( F k ( t 0 ) - S 0 ) 0, (8) F k [ F k ( t i ) - F i ( t i - 1 ) ]exp rt i + 1, (9) = 1 F k ( t l ) (exp rt l - exp rt j ) + 2 F k ( t j ) (exp rt j - exp rt p ) + 3 F k ( t p ) (exp rt p - 1), (9) k t :S 0, F k ( t 0 ), r( ) (1 - ) S 0 - (+ ) F k ( t 0 ),,,, , 0, ( ) ( t = t 0 ) ( t = t k ) S 0, - (+ ) F k ( t 0 ),4, - v, - F k ( t 0 ), S 0 e rt 0, 2 = 3 F k ( t p ) - [ F k ( t p ) - F k ( t 0 ) ] S (+ ) F k ( t 0 ) - F k ( t 0 ) v (+ ) F k ( t 0 ) S S 0 e rt 0

5 = (+ ) F k ( t 0 ) exp rt 0 + ( 1 F k ( t l ) - F k ( t 0 ) ) exp rt l + ( 2 F k ( t j ) - 1 F k ( t l ) ) exp rt j + ( 3 F k ( t p ) - 2 F k ( t j ) ) exp rt p - [ F k ( t i ) - i = 1 F k ( t i - 1 ) ]exp rt i, (10) (10), t l t j t p 1 F k ( t l ) - F k ( t 0 ) 2 F k ( t j ) - 1 F k ( t l ) 3 F k ( t p ) - 2 F k ( t j )., (+ ) F k ( t 0 ) ; F k ( t i ) - F k ( t i - 1 ) > 0 i F k ( t i ) - F k ( t i - 1 ), ; F k ( t i ) - F k ( t i - 1 ) < 0 i F k ( t i ) -. F k ( t i - 1 ),, 0,: - v S 0 e rt 0 ( 2 F k ( t j ) - 1 F k ( t l ) ) exp rt j - ( 3 F k ( t p ) - - (+ ) F k ( t 0 ) exp rt 0 - ( 1 F k ( t l ) - F k ( t 0 ) ) exp rt l - 2 F k ( t j ) ) exp rt p + [ F k ( t i ) - F k ( t i - 1 ) ]exp rt i + 3 F k ( t p ) - F k ( t p ) + F k ( t 1 ) exp rt 1 - F k ( t 0 ) exp rt 1 0, (11) - v F k ( t 0 ) 1 + S 0 e rt 0 + F k ( t 1 ) exp rt 1 - F k ( t p ) + [ F k ( t i ) - F k ( t i - 1 ) ]exp rt i - 1, exp rt 1 + (+ ) exp rt 0 - exp rt l (12) k t 0. k F k ( t 0 ) (9) (12),,,. (12) 4 : = 0106 % ; V = 2 Π;u = 0125 Π ;= 17 % ;= 5 %, 1 = 10 %, 2 = 15 %, 3 = 20 %. = 5 % ; 1 = 10 % ; 2 = 15 % 6 ; 3 = 20 %, , 5 % ,3 (Cu0209 ) ,(6) [ , ], 3, = 74178, , [ , ] = 81,, = : 5 % ;7 % ;10 % ; 15 % ;20 % ;30 %.

6 ,615 %,., ,5 %, ,17360,1570, = % = 9 %,3 (Cu0309 ) F k 17250, (6) [ , ]., = , 1000., [ , ] = 60,,, 1000, = COC,,,,,COC,, :,. : ;,;,..,,,,. : [ 1 ] Kawaller I, Koch T W. Cash and carry trading and the pricing of treasury bill futures[j ]. Journal of Futures Market, 1984, 4 (2) ; [ 2 ] Chow B G, Brophy D J. Treasury bill futures market a formulation and reinterpretation[j ]. Journal of Futures Market, 1982,2 (1) : [ 3 ] Hegde S P, Branoh B. An empirical analysis of arbitrage opportunities in the treasury bill futures market [J ]. Journal of Futures Market,1985,5 (3) : [ 4 ] Poskitt R. The pricing of bank bill futures contracts and FRA contracts in new zealand[j ]. Accounting and Finance, 1998,38 : [ 5 ] Poskite R. An intraday test of pricing and arbitrage opportunities in the New Zealand bank bill futures market[j ]. Journal of Futures Market, 2002, 22 (6) : [ 6 ] Barberis N, Thaler R. A survey of behavioral finance [ A ]ΠΠ. en Constantinides G, Harris M, Stulz R, et al. Handbook of the Economics of Finance. Elsevier Science B. V. 2003,chapter 18 : [ 7 ] Sabuhoro J B,Larue B. The market efficiency hypothesis : The case of coffee and cocoa futures[j ]. Agricultural Economics, 1997, 16 (3) : [ 8 ] Movassagh N, Modjtahedi B. Bias and backwardation in natural gas futures prices[j ]. Journal of Futures Market, 2004, 25 (3) :

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