Option Valuation of Oil & Gas E&P Projects by Futures Term Structure Approach. Hidetaka (Hugh) Nakaoka

Transcription

1 Opion Valuaion of Oil & Gas E&P Projecs by Fuures Term Srucure Approach March 9, 2007 Hideaka (Hugh) Nakaoka Former CIO & CCO of Iochu Oil Exploraion Co., Ld. Universiy of Tsukuba 1

2 Overview 1. Inroducion 2. Valuaion of Oil & Gas E&P Projecs under Uncerainy of Recoverable Reserves 3. Term Srucure of Fuures Prices and Volailiies 4. Fuures Term Srucure Approach for Opions Pricing 5. Empirical Sudy 6. Conclusion 2

3 1. Inroducion 3

4 Objecives (1) For a specific problem in E&P projecs Verifying he effec of he reserve risks, by inroducing he uncerainy ino he recoverable oil & gas reserves in he producing fields. (2) For a common problem in real opions Inroducing Fuures Term Srucure Approach, a new approach o rack underlying asse value and is volailiy for long erm projecs. 4

5 Backgrounds & Moivaions Reserve Risk ~ Uncerainy of he recoverable reserves have caused serious accouning problems o he super major oil companies. Underlying Asse Prices & Volailiy ~ Tracking problems in incomplee markes. ~ Mauriy effec of he fuures price volailiy is supposed o affec he volailiy of he underlying asse value of he long erm projec. 5

6 2. Valuaion of Oil & Gas E&P Projecs under Uncerainy of Developed Reserves 6

7 E&P Business Srucure Reserve Risk Exploraion Developmen Producion Underlying Asse Price Acreage Lease Conrac Asse Price Valuaion Opions Opions Cash Flow Valuaion of Muli-seps Sraegic Opions = Uni Value of Developed Reserves Bes Fi o Real Opions 7

8 Paddock, Siegel and Smih (1988), Opion Valuaion of Claims on Real Asses : The Case of Offshore Peroleum Leases, The Quarerly Journal of Economics ~ A pioneer in his field. ~ Combinaion of opion pricing heory and a marke equilibrium model for he underlying asse value. ~ A comprehensive work on sochasic models for he exploraion phase hrough he producion phase. Reserve Risk: considered only a he exploraion phase Underlying Asse Value: deemed o be 1/3 of spo price Volailiy: volailiy of U.S. impor oil price is applied 8

9 Reserve Risk in Oil & Gas E&P Projecs Oil & gas accumulaion is rapped in he reservoir rocks which normally lie several housands meers deep underground. Recoverable reserves are always dependen upon geophysical condiions of he reservoirs such as formaions, emperaure, pressure, how o exrac oil & gas and so on, which are he causes of he uncerainy. Sochasic Model of Developed Reserves 9

10 2-(1) Underlying Asse Value under Uncerainy of Developed Reserves Sochasic Process of Underlying Asse ValueU Assuming ha V (uni underlying asse value) follows he model of Paddock, Siegel and Smih (1988) and he developed reserves B follows GBM process, he SDE of he underlying asse value of he Block U =B V is derived from Io s lemma as follows; dv db = α = γ d +σ Bdz V d +σv dzv B B V du U = ( α γ ) d + σ dz V U dz U U dz B = ρd σ = σ + σ 2 U 2 V ρ = If B 0, i will follow Paddock, Siegel and Smih(1988). 2 B σ σ 2 V B + σ 2 B 10

11 Probabiliy Disribuion Funcion of Reserve Volume B PDF 0 lnb 11

12 12 2-(2) Developmen Opion Value Value of Undeveloped Reserve The parial differenial equaion for he value of he undeveloped reserve, Y, in he developmen phase is yielded as follows by he arbirage analysis subjec o all he parameers assumed o be deerminisic; Y is described as an American call opion under he following boundary condiions wih he sopping ime and he srike price D *, which is he esimaed developmen cos of he concession; 0 ) ( = + + U ry U Y U r U U Y Y γ σ ( ) * * * * * ), ( D U D U U Y = = + τ τ τ τ 0 ) 0, ( = Y + = ) ( ), ( * D U T U Y T T

13 2-(3) Value of he Concession before Exploraion Value of Concession Y = Y ( U ( Q), ) dp( Q) dp( Q) = p(0) (1 p(0)) f E ( Q) dq ( Q = ( Q 0) 0) Y (U (Q),) : he value of he undeveloped reserve. Q : he expeced recoverable reserves esimaed by he preliminary daa. P(Q) : he probabiliy disribuion funcion of Q. f E (Q) : he condiional probabiliy densiy funcion of Q, if Q is no zero. 13

14 Probabiliy Densiy Funcion of Q before Exploraion Probabiliy Densiy 0 Q 14

15 3. Term Srucure of Fuures Prices and Volailiies 15

16 Mauriy Effec of Volailiy Samuelson hypohesis(1965) The volailiy of fuures price reurns should increase as ime o mauriy decreases. mauriy effec of volailiy Mauriy effec is observed and modeled in such commodiy fuures prices as crude oil, agriculural commodiies, and meals. Lile evidence is observed in he financial asse prices. Term Srucure Model in Our Empirical Sudy Schwarz (1997) Two-Facor Model 16

17 Term Srucure of Volailiy of WTI Daily Rae of Reurn 17 Delivery Monh Volailiy (Daily)

18 Esimaed Volailiy Term Srucure of WTI Fuures Price Rae of Reurn Volailiy Delivery Monh 18

19 4. Fuures Term Srucure Approach for Opions Pricing 19

20 20 Fuures Term Srucure Approach The uni underlying asse price of he projec V is described as uni expecaion of an inegral of he discouned presen value of he ne cash flow f (S,B ) under he risk neural probabiliy measure subjec o S being he crude oil spo price a ime and F (u) being he fuures price wih he mauriy u ; Underlying Asse Price of he Projec Ne Cash Flow f = = = B B S S d B S f e E B V T r 0 0 0, ), ( ~ 1 b S a S f + = ) ( Assuming ha B is deerminisic and f (S ) is affine as described as, hen [ ] [ ] ( ) ) ( ) ( ~ ) ( ~ F f b F a b S S S E a S S S f E = + = + = = =

21 Underlying Asse price V V = 1 B T 0 e r f ( F ( ) 0 ) d Fuures Term Srucure Approach If he fuures prices can be inferred up o he mauriy of he projec life, hen he underlying asse price can be esimaed as he discouned value of he deerminisic ne cash flow. (1) The mauriy effec of he volailiy can be incorporaed. (2) Fiscal erms, OPEX, ec. for each projec can be incorporaed. 21

22 5. Empirical Sudy 22

23 5-(1). Underlying Asse Price of Projec X 23

24 Empirical Case Sudy ~ Projec X ~ Basic Terms of Projec X Proven recoverable oil & gas reserves: 1 billion barrels Opion o develop (pospone): 5 years Consrucion cos: $ 2.59 billion Risk-free ineres rae: 6.0% per annum Projec life: 27 years Marke price of he producs: linked wih WTI fuures price American Call Opion 24

25 Tracking of Projec X Underlying Asse Price by Fuures Term Srucure Approach Long Horizon WTI Fuures Price Long horizon WTI fuures prices are inferred from he daa of WTI fuures prices from January 1990 hrough March 2001, applying he Kalman filer o he Schwarz (1997) wo-facor model. Underlying Asse Price V Applying he above prices o he financial model of Projec X, ime series of underlying asse prices are esimaed. As a resul, he following parameers are esimaed, assuming geomeric Brownian moion; Expeced rae of reurn 2.6% per annum Volailiy 10.8% per annum Average price $4.74 per barrel 25

26 Volailiy of Projec X Tradiional Risk Measuremen As a common indusrial pracice, E&P projec owners normally evaluae heir projec risk by he volailiy of he rae of reurn of eiher spo oil prices or fuures fron monh prices. Volailiy of WTI fuures fron monh prices during January 1990 and March 2001 is 28.1% per annum. Fuures Term Srucure Approach Volailiy of Projec X during he same period is 10.8% per annum. Comparison of he Real Opions Valuaion (WTI Fron Monh Model) We compare he wo approaches in opions valuaion a differen levels of underlying asse prices, applying a binomial model. 26

27 Valuaion of Projec X as an American Call Opion Valuaion of Projec X as an American Call Opion Opion Premium ($/bbl) Underlying Asse Price ($/bbl) Valuaion of Projec X as an American Call Opion Underlying Asse Price Term Srucure Model WTI Fron Monh Model

28 5-(2) Developmen Opion Value under Uncerainy of Developed Reserves 28

29 Volailiy of Underlying Asse Price U under Uncerainy of Developed Reserves σ = σ + σ 2 U 2 V 2 B V : Volailiy of Uni Value of Developed Reserve B : Volailiy of Developed Reserve Volume Table1. Volailiy Change in Underlying Asse Price wih Change in Volailiy of Reserve Volume B 0.0% 2.5% 5.0% 7.5% 10.0% 12.5% 15.0% V 10.8% 10.8% 10.8% 10.8% 10.8% 10.8% 10.8% U 10.8% 11.1% 11.9% 13.2% 14.7% 16.5% 18.5%

30 Impac on Developmen Opion Value by Uncerainy of Developed Reserves Table2. Impac on Developmen Opion Value by Uncerainy of Developed Reserves Underlying Asse Price B = 0% ,090 1,580 2,080 2,580 3,080 B = 5% ,090 1,580 2,080 2,580 3,080 B = 10% ,100 1,590 2,080 2,580 3,080 B = 15% ,150 1,620 2,100 2,590 3,080 (million dollars) 30

31 Impac on Developmen Opion Value by Uncerainy of Reserves Developmen Opion Premium ($MM) 1,800 1,600 1,400 1,200 1, Underlying Asse Price ($/bbl) σb = 0% σb = 5% σb = 10% σb = 15% 31

32 5-(3) Value of Concession under Uncerainy of Developed Reserves 32

33 Value of Concession under Uncerainy of Developed Reserves Table3. Value of Concession under Uncerainy of Developed Reserves Underlying Asse Price ($/bbl) U 10.8 MM$) ,049 1,249 U 18.5 MM$) ,054 1,251 (million dollars) 33

34 Value of Concession under Uncerainy of Developed Reserves 700 Value of Concession ($MM) No Reserve Risk Volailiy 10.8 Wih Reserve Risk Volailiy Underlying Asse Price ($/bbl) 34

35 6. Conclusion 35

36 Conclusion (1) In his paper, we derive sochasic equaions for he underlying asse value of he E&P projec under he uncerainy of he developed reserves. We verify ha such reserve risks can give significan impac on he developmen opions value and he value of he concession wrien over he underlying asse. (2) In order o solve racking problems of he underlying asse prices, we inroduce a new pracical approach of Fuures Term Srucure Approach, which verifies ha he volailiy of he oil & gas E&P projec should be much smaller han hose esimaed by he radiional risk measuremen due o he mauriy effec of he volailiy of he fuures prices. 36