Valuing Real Options on Oil & Gas Exploration & Production Projects

Transcription

1 Valuing Real Opions on Oil & Gas Exploraion & Producion Projecs March 2, 2006 Hideaka (Hugh) Nakaoka Former CIO & CCO of Iochu Oil Exploraion Co., Ld. Universiy of Tsukuba 1

2 Overview 1. Inroducion 2. Wha are he Risks in Oil Business 3. Real Opions for E&P Projecs 4. Valuaion of Oil & Gas E&P Projecs 5. Term Srucure of Fuures Prices and Volailiies 6. Fuures Term Srucure Approach for Opions Pricing 7. Conclusion 2

3 1. Inroducion 3

4 Purpose In his presenaion, we will inroduce: A new pracical approach for business praciioners o rack underlying asse value and is volailiy for real opions valuaion of oil & gas E&P projecs. 4

5 Problems in Real Opions Incomplee Marke ~ Underlying asse markes are normally incomplee. Underlying Asse Prices & Volailiy ~ Then, how do we pracically esimae underlying asse prices and heir volailiies? 5

6 Pracical Soluions We will inroduce a new pracical approach: Fuures Term Srucure Approach In his approach, we will ~ esimae erm srucure of fuures prices and volailiies wih long mauriies up o projec life, using an appropriae erm srucure model, ~ esimae underlying asse prices, applying such erm srucure o a financial model for a respecive projec, and ~ esimae volailiy of underlying asse price rae of reurn 6

7 Seps o a New Approach We will (1) review and refurbish heoreical frameworks for opions valuaion of oil & gas E&P projecs, (2) review and summarize heoreical frameworks of erm srucure of fuures prices and volailiies in he lieraure, (3) conduc empirical sudies on oil fuures erm srucure, and (4) presen a new approach of Fuures erm srucure approach wih some empirical sudies 7

8 2. Wha are he Risks in Oil Business 8

9 Upsream ~ Downsream in Oil Business Source: Peroleum Associaion of Japan Source: RasGas 9

10 Various Risks in Oil Business Upsream Oil Price Risk, Exploraion Risk, Developmen Risk, Reserve Risk, Operaional Risk, Counry Risk, Environmenal Risk, ec. Downsream Oil Price Risk, Crude Oil Procuremen Risk, Transporaion Risk, Operaional Risk, Markeing Risk, Legal Risk, Poliical Risk, Environmenal Risk, ec. 10

11 Risk Managemen in Oil Business Commodiy Business Sraegic Invesmen The mos acively raded and volaile fuures marke Huge sraegic long erm invesmen increases in risks Increasing risks in volaile markes Unmanageable by DCF Needs for sraegic decision making by Real Opions Pracical problems need o be seled 11

12 3. Real Opions for E&P Projecs 12

13 E&P Business Srucure Exploraion Developmen Producion Acreage Lease Conrac Opions Opions Bes Fi o Real Opions Asse Price Valuaion Cash Flow Valuaion of Muli-seps Sraegic Opions 13

14 Problems in Valuaion by DCF Exploraion Developmen Producion Acreage Lease Conrac Opions Opions Valuaion by DCF (1) Impossible o value flexibiliy (2) Difficul o presume iming o exercise (3) Impossible o forecas an Oil Price (4) No so easy o selec a Discoun Facor 14

15 Real Opions Approach for E&P Projecs Underlying Asse Curren value of a uni of developed reserves Opion o Pospone Opion o Expand American Call Opion wih an Exercise Price a Consrucion Cos Opion o Conrac Opion o Abandon American Pu Opion wih an Exercise Price a Cancellaion Cos Compound Opions Combinaion of he Above Opions 15

16 4. Valuaion of Oil & Gas E&P Projecs 16

17 Framework for he Valuaion of Claims Paddock, Siegel, and Smih (1988) = PSS Se up a heoreical framework based on he approach by Paddock, Siegel, and Smih (1988) Opion Valuaion of Claims on Real Asses: The Case of Offshore Peroleum Leases PSS Mehodology Combinaion of opion pricing heory and a marke equilibrium model for he underlying asse Our Approach We refurbish and exend PSS model wih he addiion of he sochasic behavior of he volume of developed oil & gas reserves 17

18 Curren per uni value of undeveloped reserves X ( V, ; D( Q)) 1 = E Q T Q: recoverable oil & gas reserves F(Q): probabiliy disribuion funcion over reserves D(Q): per uni developmen cos e α V ( u ) f ( Vu, Bu, u ; D( Q)) duv = V, Expeced value of oal undeveloped reserves X ( V ) = QX ( V, ; D( Q)) df( Q) f(v u,b,u): insananeous per uni ime ne payoff from holding he reserves V u : value of a uni volume of developed oil & gas reserves B u : random variable for he volume of developed oil & gas recoverable reserves α V *: expeced rae of reurn o he owner B = Q 18

19 Marke Equilibrium Model Assuming a diffusion process for rae of reurn and volume of reserves, he ne payoff can be wrien as follows, since i is a composie of profis from producion and capial gains; f d = α V d + σ V dz db V = γ Bd + σ B Bdz B BV dz dz V B = 0 f d = γ B P d σ B P dz + ( 1 γ d + σ dz ) B ( V + dv ) B { } { V } B Underlying asse price V The above equaions yield he process of V (value of a uni volume of producing developed oil & gas reserves) as follows; dv db = αv d + σ dz = γ d +σ V V Bdz dz dz d B = ρ V B V B 2 2 P V ) 2 2 σ δ σ B Bδ α α δ σ = σ ρ = V = V δ V = γ ( Parameers of B should be deermined geologically. B V V + 2 γ B B (P : afer-ax operaing profi per uni) γ σ + σ δ V B Pracical Problems How do we esimae V? 19

20 20 *A he F/S and developmen phase, per uni value of undeveloped reserves X can be wrien as follows, using equilibrium analysis of risk-free porfolio (all he parameers assumed deerminisic); * X will be evaluaed as an opion o pospone, expand, conrac, abandon, or compound opions wih appropriae boundary condiions. 0 ) ( = + + V rx V X V r V V X X δ σ PDE for Undeveloped Reserves

21 5. Term Srucure of Fuures Prices and Volailiies 21

22 Mauriy Effec of Volailiy Samuelson hypohesis(1965) The volailiy of fuures price reurns should increase as ime o mauriy decreases. ( mauriy effec of volailiy ) Gibson and Schwarz (1990) The sochasic convenience yield, which is mean-revering and posiively correlaed wih he spo price, implies mauriy effec of volailiy in crude oil fuures prices. Mean Reversion Process Mean reversion process is observed in such commodiy fuures prices as crude oil, agriculural commodiies, and meals. Lile evidence is observed in he financial asse prices. 22

23 Term Srucure of WTI Fuures Prices monh 3monh 5monh 7monh 9monh 11monh 13monh 15monh 17monh Delivery Monh 1991/1Q 1996/1Q 2000/1Q WTI Fuures Price ($/bbl)

24 Term Srucure of WTI Daily Rae of Reurn monh 3monh 5monh 7monh 9monh 11monh 13monh 15monh 17monh Delivery Monh 1991/1Q 1996/1Q 2000/1Q Daily Rae of Reurn

25 Term Srucure of Volailiy of WTI Daily Rae of Reurn monh 3monh 5monh 7monh 9monh 11monh 13monh 15monh 17monh Delivery Monh 1991/1Q 1996/1Q 2000/1Q Volailiy (Daily)

26 Two Differen Approaches for Term Srucure of Fuures Prices and Volailiies Sochasic Mean-Revering Convenience Yield Approach Gibson and Schwarz (1990) Schwarz (1997) Hilliard and Reis (1998) ec. HJM Forward Curve Approach Milerssen and Schwarz (1998) Koekebakker and Lien (2004) ec. Term Srucure Model in Our Empirical Sudy Schwarz (1997) Two-Facor Model 26

27 Schwarz (1997) Two-Facor Model ds = ( μ δ ) Sd + σ Sdz 1 dδ = κ( α δ ) d + σ dz dz dz = ρd Jamshidian and Fein (1990) and Bjerksund (1991) have shown he following closed-form soluion for he fuures price. κt 1 e F( S,, T ) = S exp + A( T ) δ δ κ κt (1 e ) 1 e σ F ( T ) = σ1 + σ 2 2σ 1σ 2ρ 2 κ κ 1 F F T ( T ) = r 2 1 σ 2 ˆ κ σ1σ ρ κ α 2 κt (forward cos of carry) (Schwarz exended he wo-facor model o he hree-facor model, including Ornsein-Uhlenbeck ype sochasic ineres rae process. Hilliard and Reis (1998) applied HJM ineres rae process and furher exended he model o he hree-facor model wih jump diffusion process.) 27

28 Empirical Sudy Under he Schwarz (1997) wo-facor model, parameers of he model are calibraed by he mehod of leas squares, using daa of he fron monh and he 18 h monh of WTI (Wes Texas Inermediae Crude Oil) fuures prices from January 1990 hrough March Parameer Esimae μ κ α σ(1) σ(2) ρ λ

29 Esimaed Volailiy Term Srucure of WTI Fuures Price Rae of Reurn 30.00% 25.00% Volailiy 20.00% 15.00% 10.00% 5.00% 0.00% Delivery Monh 29

30 Esimaed Term Srucure of WTI Fuures Prices WTI Fuures Prices ($/bbl) Delivery Monh Backwardaion Conango 30

31 Esimaed Volailiy Term Srucure of WTI Fuures Price Rae of Reurn 30.00% 25.00% Volailiy 20.00% 15.00% 10.00% 5.00% 0.00% Delivery Monh 31

32 Esimaed Term Srucure of WTI Fuures Prices WTI Fuures Prices ($/bbl) Delivery Monh 32

33 6. Fuures Term Srucure Approach for Opions Pricing 33

34 Problems in Real Opions Incomplee Marke ~ Underlying asse markes are normally incomplee. Underlying Asse Prices & Volailiy ~ Then, how do we pracically esimae underlying asse prices and heir volailiies? 34

35 Tracking of he Underlying Asse Price and Volailiy by PSS (1) The value of he developed recoverable reserves is assumed o be 1/3 of he crude oil spo price. (2) Volailiy of he rae of reurn of he underlying asse price is assumed o be replaced by he volailiy of he rae of reurn of he U.S. impored crude oil price. Problems wih PSS Approach Acual value of reserves differs field by field. Difficul o calibrae he parameers of he model, since he acual rue ne payoff funcion is oo complex o represen by a racable simple mahemaical funcion. 35

36 Financial Model of E&P Projec Financial Model Projec economics can be calculaed by a financial model of a respecive projec, which incorporaes idiosyncraic variables such as fiscal erms, reserves, producion, CAPEX, OPEX, crude oil prices, and so on. Ne Payoff Funcion Financial model conains per uni ime ne payoff funcion g(f (u),b u,u; D(Q)), which approximae he rue funcion of he projec as follows (F (u) is a fuures price a ime wih mauriy u); E T = E e V α ( u ) T e V α ( u f ( V u, Bu, u ; D( Q)) duv = V, B = Q ) g( F u B u D Q duv = V B = Q ( ), u, ; ( )), 36

37 Pracical Soluions for Tracking We will inroduce a new pracical approach: Fuures Term Srucure Approach In his approach, we will (1) esimae erm srucure of fuures prices and volailiies, using an appropriae erm srucure model, (2) esimae fuures prices of ulra-long mauriies up o projec life, using ime series daa of fuures prices (3) esimae ime series of underlying asse prices, applying esimaed fuures prices o a financial model of a respecive projec, and (4) esimae volailiy of underlying asse price rae of reurn. 37

38 Empirical Sudy (1) ~ Valuaion of Projec X as an American Call Opion ~ 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 underlying asse: deermined by WTI fuures price 38

39 Tracking of Projec X Underlying Asse by Fuures Term Srucure Approach Long Horizon WTI Fuures Price Long horizon WTI fuures prices are esimaed, using he Schwarz (1997) wo-facor model calibraed by he daa of WTI fuures prices from January 1990 hrough March Underlying Asse Price 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 0.31% per annum Volailiy 6.81% per annum Average price $4.02 per barrel 39

40 7.00% Hisogram of he Underlying Asse Price Rae of Reurn % -4.00% -3.00% -2.00% -1.00% 0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% Rae of Reurn (%) -6.00% Frequency

41 Volailiy of Projec X Tradiional Approach (WTI Fron Monh Model) 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 28.05% per annum. Fuures Term Srucure Approach Volailiy of Projec X during he same period is 6.81% per annum. Comparison of he Real Opions Valuaion Projec X can be evaluaed as an American call opion. We compare he wo approaches a differen underlying asse prices, using binomial model. 41

42 Valuaion of Projec X as an American Call Opion 3.50 Valuaion of Projec X as an American Call Opion Opion Premium ($/bbl) Underlying Asse Price ($/bbl) Term Srucure Model WTI Fron Monh M d l Valuaion of Projec X as an American Call Opion Underlying Asse Price Term Srucure Model WTI Fron Monh Model

43 Empirical Sudy (2) ~ Valuaion of Projec X as Compound Opions ~ New Terms of Projec X Afer projec owners decided o conduc Fron End Engineering Design (FEED) a he expense of $ 90 million, Projec X is assumed o have he following new schemes; Proven recoverable oil & gas reserves: 1 billion barrels Opion o abandon: 2 years (a he expense of Feed cos) Consrucion cos: $ 2.59 billion (including FEED cos) Opion o conrac by 50%: 2 years (Consrucion cos reduced by 22%) Opion o expand by 50%: 5 years (Consrucion cos increased by 36%) Risk-free ineres rae: 6.0% per annum Projec life: 27 years Marke price of he underlying asse: deermined by WTI fuures price 43

44 Valuaion of Projec X as Compound Opions Valuaion of Projec X as Compound Opions 2.00 Opion Premium ($/bbl) Underlying Asse Price ($/bbl) Term Srucure Model WTI Fron Monh Model Valuaion of Projec X as Compound Opions Underlying Asse Price Term Srucure Model WTI Fron Monh Model

45 Analysis of he Empirical Sudy Boh empirical sudies have shown significan difference in he Real Opions valuaion beween Tradiional Approach and Fuures Term Srucure Approach. The difference appears more significan, when he iniial underlying asse price goes near or below he exercise price. A $ 2.00 per barrel, he difference is 38 cens per barrel (19% of he underlying asse price) in Sudy (1), and i is 30 cens per barrel (15% of he same) in Sudy (2). The difference becomes considerably narrowed down, only when he iniial underlying price goes far above he exercise price, however, we will seldom see such a rosy siuaion in he acual business opporuniies. 45

46 Conclusion (1) This paper refurbishes and exends he sochasic differenial model of Paddock, Siegel and Smih (1988) wih he addiion of he sochasic behavior of he volume of developed oil & gas reserves. (2) In order o solve a pracical problem of racking he underlying asse prices and he volailiy of he asse price rae of reurn, his paper inroduces a new pracical approach of Fuures Term Srucure Approach, which can esimae he asse prices by ime series daa of fuures prices, using a erm srucure model of fuures prices ogeher wih a financial model of he projec. 46

47 (3) The empirical sudies clearly indicae ha he rae of reurn of he underlying asse price of oil & gas E&P projecs is much less volaile han ha of he crude oil fuures fron monh conrac, which is normally applied o he risk analysis of he E&P projecs in Tradiional Approach. (4) The empirical sudies also indicae ha Fuures Term Srucure Approach can no only be a pracical soluion for he racking problem of he underlying asse prices and volailiies for long horizon invesmens, bu i can also provide an appropriae approach o avoid overesimaion of he Real Opions valuaion, which is very likely o be caused by Tradiional Approach. 47