The objective of this paper is to develop a methodology to assess the impact of fiscal risk, the risk of contractual non-performance by a host government, on the value and stability of contracts for petroleum investment. In the proposed fiscal risk model, the host government may appropriate a share of excess profits (resulting from perceived price or discovery windfalls) higher than that specified in stated contract terms. A valuation framework similar to that used to price options and futures in financial markets is used. Various components of the project are valued as contingent claims on the revenue stream of the developed field. Four fiscal regimes -- royalty, production sharing, service and resource rent tax -- were designed to give the same asset value to the foreign oil company under stated contract terms; however, when fiscal risk is taken into account, this value can be substantially lower. The royalty and production-sharing contracts are quite unstable because a large fraction of the initial value accruing to oil companies under stated contract terms comes from the possibility of large discoveries, where fiscal risk is most severe. The resource rent tax and the service contract are more stable because both fiscal regimes generate the bulk of oil company value from the possibility of small and medium discoveries. The stability of the production-sharing contract can be enhanced substantially if the host government share of profit oil is set by a progressive sliding-scale schedule. In general, contract stability is enhanced if the government explicitly bears much of the oil price and discovery risk.