The increasing development of offshore wind parks in the European offshore territory may lead to meshed offshore grids in which each wind park might be connected to several countries. Such offshore grids could be subject to various regulatory regimes, depending on the degree of cooperation between the respective countries. This study focuses on how investors in wind parks and transmission systems are affected by the choice of regulatory regime in offshore grids with one to four countries connected. In order to capture the uncertainties related to the exposure to market prices as well as risks related to line failures, we develop a stochastic model for an exemplary wind park and offshore grid. This yields the real option values of operational flexibility from additional connections. Simulation results show that the choice of regulatory regime, including market access and pricing rules, can have a significant impact on the value of a wind park and on the value of the interconnection capacity in the offshore grid. The impact can both be positive and negative, implying a complex incentive structure for the involved actors. If contrary effects are not reflected in the remuneration level of a wind park, for example in the price premium level, investment incentives could either be diminished or the wind park could incur windfall profits. Both cases are socio-economically suboptimal as they may pose additional cost to the system. Policy makers should consider these findings when designing the regulatory regime and level of support in an offshore grid in order to maintain an effective and efficient development of offshore wind in Europe.