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Wojciech Maliszewski

. The initial oil production has mean μ 0 = μ P , 0 Q and variance σ 0 2 = σ P , 0 2 Q 2 . With these assumptions, Engel and Valdez (2001) derived a formula for the optimal government consumption under oil-price uncertainty, which is a function of the optimal POIM consumption without oil-price uncertainty, and the parameters governing uncertainty in the oil-price process. The government is assumed to re-optimize at the beginning of each period, and the function takes the following form: g 0 ( σ 0 2 , σ v 2

Mr. Noureddine Krichene
Crude oil prices have been on a run-up spree in recent years. Their dynamics were characterized by high volatility, high intensity jumps, and strong upward drift, indicating that oil markets were constantly out-of-equilibrium. An explanation of the oil price process in terms of the underlying fundamentals of oil markets and world economy was provided, viewing pressure on oil prices mainly as a result of rigid crude oil supply and an expanding world demand for crude oil. A change in the oil price process parameters would require a change in the underlying fundamentals. Market expectations, extracted from call and put option prices, anticipated no change, in the short term, in the underlying fundamentals. Markets expected oil prices to remain volatile and jumpy, and with higher probabilities, to rise, rather than fall, above the expected mean.
Mr. Noureddine Krichene

jumps. The distribution had also fat tails, meaning that large jumps tended to occur more frequently than in the normal case. These empirical findings about daily oil futures prices were typical of financial time series as noted in Clark (1973) , Fama (1965) , and Mandelbrot (1963) . These facts suggested modeling the oil price process as a jump-diffusion or, in a more general way, as a Levy process ( Cont and Tankov, 2004 ). Figure 2. Daily Crude Oil Price Returns Distribution, Jan 2, 02-July 7, 06. Descriptive statistics: mean = 0.116; standard deviation

Chang Ma and Mr. Fabian Valencia
Over the past two decades, Mexico has hedged oil price risk through the purchase of put options. We examine the resulting welfare gains using a standard sovereign default model calibrated to Mexican data. We show that hedging increases welfare by reducing income volatility and reducing risk spreads on sovereign debt. We find welfare gains equivalent to a permanent increase in consumption of 0.44 percent with 90 percent of these gains stemming from lower risk spreads.
Mr. Noureddine Krichene
Following record low interest rates and fast depreciating U.S. dollar, crude oil prices became under rising pressure and seemed boundless. Oil price process parameters changed drastically in 2003M5-2007M10 toward consistently rising prices. Short-term forecasting would imply persistence of observed trends, as market fundamentals and underlying monetary policies were supportive of these trends. Market expectations derived from option prices anticipated further surge in oil prices and allowed significant probability for right tail events. Given explosive trends in other commodities prices, depreciating currencies, and weakening financial conditions, recent trends in oil prices might not persist further without triggering world economic recession, regressive oil supply, as oil producers became wary about inflation. Restoring stable oil markets, through restraining monetary policy, is essential for durable growth and price stability.
Mr. Noureddine Krichene

10, with prices rising progressively to cross US$96/barrel mark in October 2007, showing no sign for stability around a mean. The upward trend became predictable and was the longest upward trend in post-war oil prices. Past upward trends lived on average two to three years, while the present one has spanned so far more than four years. Denoting oil price by St and applying an autoregressive moving average (ARMA) representation, the structure of the oil price process has changed considerably as conveyed by the two regressions below, namely in the second sub

Mr. Noureddine Krichene

Front Matter Page African Department Authorized for distribution by Benedicte Vibe Christensen Contents I. Introduction II. Recent Evolution of Oil Prices III. Modeling Oil Prices as Levy Process IV. Oil Price Process as Normal Inverse Gaussian Process V. Estimation of Oil Price Process as a Normal Inverse Gaussian Process VI. Market Incompleteness and Esscher Transform VII. Density Forecast of Crude Oil Prices: The Inverse Problem VIII. Conclusions Tables 1. Descriptive Statistics for Oil Price Returns 2. Oil Price as Normal

Wojciech Maliszewski

Front Matter Page Fiscal Affairs Department Authorized for distribution by Mark Horton Contents I. Introduction II. Fiscal Rules for OPCs A. Optimizing Rules B. Ad hoc Rules III. Numerical Comparisons A. Setup and Assumptions B. Results IV. Conclusions Tables 1. Initial Conditions 2. Model Parameters 3. Comparison of Policy Rules (Baseline) 4. Comparison of Policy Rules (Alternative Specification for the Oil Price Process) Figures 1. PIM and POIM Rules for the Mature Oil Producer 2. PIM and POIM Rules for the

Mr. Nikolay Aleksandrov, Mr. lajos Gyurko, and Mr. Raphael A Espinoza

the Oil Price Process (OLS on Yearly Data for the Period 1957–2008) 2. Parameters of the Schwartz-Smith (2000) Price Process Estimated on Futures Data 3. Annualized Parameters of the Extraction Cost Process (OLS on quarterly Data for the Period 1999–Q1 to 2009–Q1 4. Model for Proven Reserves (Standard Errors in Parentheses 5. Oil Production Capacity 6. Added Value by Expanded Capacity 7. Added Value by Expanded Capacity and Increased Access to Reserve 8. Determinants of Cuts in Production During the Crisis of 2008–2009 References Figures 1

Chang Ma and Mr. Fabian Valencia

A Proof of Proposition 1 B Proof of Proposition 2 C Proof of Proposition 3 D Proof of Proposition 4 III Algorithm IV Estimation of Oil Price Process V Option Pricing Tables 1 Actual Strike Prices from Options 2 Parameters 3 Stochastic Steady State in the Hedging and No-hedging Economies 4 Sensitivity Analysis 5 Welfare Gains from Selling Oil Forward 6 Risk Averse Investors: Hedging and No-hedging Economies Figures 1 Oil Production, Oil Prices, and Sovereign Spreads 2 Mexico’s Oil Hedging Program 3 Two-period Model 4 Welfare