スプレッド・オプション評価公式を用いた裁定取引の可能性―電力市場のケース― 藤原 浩一,新関 三希代
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1 Black and Scholes kfujiwar@mail.doshisha.ac.jp
2 Deng, Johnson and Sogomonian 1999 Margrabe Deng, Johnson and Sogomonian 1999 Margrabe 1978 Black and Scholes 1973 BS BS
3 generating transmission derivate General Electric Edison Electric Light Company 1990
4 PX Power Exchange ISO Independent System Operator PX ISO ISO PX ISO PX ISO PX ISO / kwh 5.9 / kwh 6.6 / kwh 9.2 / kwh
5 NYMEX New York Mercantile Exchange NYMEX 2. 2 spark spread NYMEX
6 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
7 Henry Hub Btus NYMEX ,000 1kw 8,000 Btus 8,000 1, Mwh 10,000 million Btus NYMEX /10,000 = NYMEX Henry Hub British thermal unit Btu
8 Mwh $20/Mwh = $73, ,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 Henry Hub Btus NYMEX $16/Mwh 3 7 $1.60/mmBtu ,000 mmbtu $1.60/mmBtu = $48, 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 Mwh
9 $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)
10 Se Sg Kh Sg Kh 8 Kh Se 1 Kh Sg 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
11 Kh H 3 3 Kh H Se Kh Sg 0 4 Kh Se Kh Sg 5 H Se / Sg Kh H 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
12 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
13 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
14 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)
15 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
16
17
18
19 Black, F. and M. Scholes, (1973) The Pricing of Options and Corporate Liabilities, Journal of Political Economy, Vol.81, pp 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 Margrabe, W., (1978) The Value of an Option to Exchange One Asset for Another, The Journal of Finance, Vol.33, pp NYMEX, (2003) CRACK SPREAD HANDBOOK, NYMEX H.P., Vasicek, O., (1977) An Equilibrium Characterization of the Term Structure, Journal of Financial Economics, Vol.5, pp , 2004.
20 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.
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