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Visual FAQ’s on Real Options Celebrating the Fifth Anniversary of the Website: Real Options Approach to Petroleum Investments http://www.puc-rio.br/marco.ind/ By: Marco Antônio Guimarães Dias Petrobras and PUC-Rio, Brazil Real Options 2000 Conference Capitalizing on Uncertainty and Volatility in the New Millennium September 25, 2000  Chicago

Visual FAQ’s on Real Options ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Visual FAQ’s on Real Options: 1 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Real Options Premium ,[object Object]

Visual FAQ’s on Real Options: 2 ,[object Object],[object Object],[object Object],[object Object]

Timing Suite : Real Options Spreadsheets ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

“Timing”: Standard Version

“Timing” Standard Version: Charts

Timing Suite: Others Spreadsheets ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Visual FAQ’s on Real Options: 3 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Uncertainty Over the Expansion Value ,[object Object],[object Object],[object Object]

Option to Expand the Production ,[object Object],[object Object],[object Object]

Real Options Asymmetry and Valuation + = Prospect Valuation Traditional Value =  5 Options Value(T) = + 5 ,[object Object]

E&P Process and Options ,[object Object],[object Object],Oil/Gas Success Probability = p Expected Volume of Reserves = B Revised Volume = B’ ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Option to Expand the Production ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Modeling the Option to Expand ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Visual FAQ’s on Real Options: 4 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Geometric Brownian Motion Simulation ,[object Object],[object Object],[object Object],[object Object],[object Object],P t = P 0 exp{ (    )  t +  P t = P 0 exp{ ( r    )  t + 

Risk-Neutral Simulation x Real Simulation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Incomplete Markets and Real Options ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Visual FAQ’s on Real Options: 6 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Geometric Brownian Motion (GBM) ,[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],Mean-Reverting Process

Nominal Prices for Brent and Similar Oils (1970-1999) ,[object Object],Jumps-up Jumps-down

Mean-Reversion + Jumps for Oil Prices ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],(the probability of jumps) (jump size) where:

Equation for Mean-Reversion + Jumps ,[object Object],mean-reversion drift: positive drift if P < P negative drift if P > P { uncertainty over the continuous process (reversion) { variation of the stochastic variable for time interval dt uncertainty over the discrete process (jumps) continuous ( diffusion ) process discrete process ( jumps )

Mean-Reversion x GBM: Option Premium ,[object Object],[object Object],Reversion in all cases: to 20 $/bbl

Mean-Reversion with Jumps x GBM ,[object Object],[object Object]

Mean-Reversion x GBM ,[object Object],[object Object]

Duopoly Entry under Uncertainty ,[object Object],[object Object]

Other Example: Oil Drilling Game ,[object Object],[object Object],[object Object],[object Object],Company X tract Company Y tract

Visual FAQ’s on Real Options: 8 ,[object Object],[object Object],[object Object],[object Object],[object Object]

Sequential Options (Dias, 1997) ,[object Object],[object Object],[object Object],( Wildcat Investment ) ( Developed Reserves Value ) ( Appraisal Investment: 3 wells ) ( Development Investment ) Note: in million US$ “ Compact Decision-Tree” EMV =  15 + [20% x (400  50  300)]  EMV =  5 MM$

Sequential Options and Uncertainty ,[object Object],[object Object],[object Object]

Option to Abandon the Project ,[object Object],[object Object],[object Object],[object Object],[object Object],(Values in millions) $ 2.25 stopping development $ 6 stopping appraisal $ 8.25 total EMV gain

Thresholds: Optimum and Sub-Optima ,[object Object]

Optima Region ,[object Object],[object Object]

Conclusions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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