In oil-dependent countries, a major issue is how to stabilize fiscal spending when government revenue fluctuates along with the international price of oil. A stabilization fund would allow the government to pull through an oil price trough and absorb windfall revenue when prices are high. This paper focuses on two key issues. First, the paper proposes to base government spending on moving averages of past oil prices that are shown to behave nearly as a random walk. Second, it uses Monte Carlo simulations of a fiscal policy model to look at the probability that a given level of assets in the stabilization fund is exhausted over a certain number of years. The simulations show that with a fiscal policy based on moving averages over three to five years, a stabilization fund of about 75 percent of 2004 oil revenue would be adequate, which, in Nigeria, would equate to US$16-18 billion.