403 81 1 Black and Scholes 1973 Email:kfujiwar@mail.doshisha.ac.jp
82 404 58 3 1 2 Deng, Johnson and Sogomonian 1999 Margrabe 1978 2 Deng, Johnson and Sogomonian 1999 Margrabe 1978 Black and Scholes 1973 BS BS 1 2 2000 3 21
405 83 2 3 4 2 2. 1 generating transmission derivate General Electric Edison Electric Light Company 1990
84 406 58 3 3 PX Power Exchange ISO Independent System Operator PX ISO ISO PX ISO PX ISO PX ISO 3 1999 3.9 / kwh 5.9 / kwh 6.6 / kwh 9.2 / kwh 1.5 2000 2004
407 85 NYMEX New York Mercantile Exchange NYMEX 2. 2 spark spread NYMEX
86 408 58 3 Emery and Liu 2002 Palo Verde PV California-Oregon Border COB Henry Hub 4 PV COB mean reversion 5 Emery and Liu 2002, p102. IPP 4 4 Emery and Liu 2002 5 2004
409 87 4 25 Henry Hub 7 100 Btus 1.45 6 7 1 20 NYMEX 2003 1 1 1 1 1 1 1 8,000 1kw 8,000 Btus 8,000 1,000 736Mwh 10,000 million Btus NYMEX 2003 8 736/10,000 = 0.59 5 3 6 NYMEX Henry Hub British thermal unit Btu
88 410 58 3 4 25 5 736 Mwh $20/Mwh = $73,600 3 10,000 mmbtu $1.45/mmBtu = $43,500 ($73,600 - $43,500)/(5 736 Mwh = 3,680) = $8.18/Mwh 5 7 $20/Mwh 3 7 $1.45/mmBtu 7 7 26 Henry Hub 7 100 Btus 1.60 1 16 NYMEX 2003 4 25 5 7 $16/Mwh 3 7 $1.60/mmBtu 7 26 3 10,000 mmbtu $1.60/mmBtu = $48,000 5 736 Mwh $16/Mwh = $58,880 ($48,000 -$58,880)/(5 736 Mwh = 3,680) = $2.96/Mwh $8.18 $2.96 $5.22/Mwh $5.22/Mwh 7 5 736 Mwh
411 89 $20/Mwh $16/Mwh $4/Mwh $5.22/Mwh $1.22/Mwh 3 BS S K CT CT max(s K,0) K S S K 0 S K S K CT max(se Kh Sg,0)
90 412 58 3 Se Sg Kh Sg Kh 8 Kh Se 1 Kh Sg 1 2 1 BS Kh Sg Se Kh Sg 0 Se Sg Kh Sg BS K Kh Sg Se Kh Sg 0 1 Kh Se Kh Sg 2 Se / Sg H Se / Sg 8
413 91 Kh H 3 3 Kh H Se Kh Sg 0 4 Kh Se Kh Sg 5 H Se / Sg Kh H 6 3 6 Kh H S K H Kh H Kh 9 PT PT max(kh Sg Se,0) 9 Deng, Johnson and Sogomonian 1999 implied heat rate
92 414 58 3 Kh Sg Se Kh Sg Se 0 H Kh Kh H H Kh BS BS non-storable Deng, Johnson and Sogomonian 1999 Futures Based Method of Replicating Derivatives
415 93 BS Fe 10 Fg 11 Vasicek 1977 dfe e ( e ln(fe))fedt e (t)fedw e dfg g ( g ln(fg))fgdt g (t)fgdw g e g e g W e W g e (t) g (t) t 10 COB 11 Henry Hub
94 416 58 3 BS X a a(x,t) b b(x,t) dx(t) a dt b W(t) X(t) t V(t) g(x(t),t) 12 g 1 dv(t) a+2 X 2 g g b+ X 2 t g dt+ b dw(t) X BS V(t) C(Fe,Fg,t) Fe Fg C exp r(t t) [Fe N(d 1 ) Kh Fg N(d 2 )] 12 X(t) V(t) V(t) = g(x(t),t) dv(t)
417 95 F ln e 2 (T t) +v Kh Fg 2 d 1 v(t t) d 2 d 1 v(t t) T t e(s) 2 ( 2 e (s) 2 g(s))ds v 2 T t N( ) (T t) T BS v BS 4 3
96 418 58 3 2
419 97 2 5 2
98 420 58 3
421 99 Black, F. and M. Scholes, (1973) The Pricing of Options and Corporate Liabilities, Journal of Political Economy, Vol.81, pp.637-659. Deng, S., B. Johnson and A. Sogomonian, (1999) Spark Spread Options and the Valuation of Electricity Generation Assets, Proceeding of the 32nd Hawaii International Conference on System Science. Emery, G.W. and Q. Liu, (2002) An Analysis of the Relationship Between Electricity and Natural-Gas Futures Prices, The Journal of Futures Markets, Vol.22, pp. 95-122. Margrabe, W., (1978) The Value of an Option to Exchange One Asset for Another, The Journal of Finance, Vol.33, pp.177-186. NYMEX, (2003) CRACK SPREAD HANDBOOK, NYMEX H.P., http://www.nymex.com. Vasicek, O., (1977) An Equilibrium Characterization of the Term Structure, Journal of Financial Economics, Vol.5, pp.177-188., 2004.
100 422 58 3 The Doshisha University Economic Review Vol.58 No.3 Abstract Koichi FUJIWARA, and Mikiyo kii NIIZEKI, The Possibility of Arbitrage Trading by the Spread Options: The Case of Electricity Market The spark spread options formula becomes important with the liberalization of the electricity market. However, electricity is non-storable and its price has a mean reversion, so we can not apply the Black and Scholes methodology for deriving the spread options formula. In this paper, we discuss the derivation methodology of the spark spread options developed by Deng, Johnson and Sogomonian, and the possibility of arbitrage trading.