Abstract-Recent studies show that the fast growing expansion of wind power generation may lead to extremely high levels of price volatility in wholesale electricity markets. Storage technologies, regardless of their specific forms e.g. pump-storage hydro, large-scale or distributed batteries, are capable of alleviating the extreme price volatility levels due to their energy usage time shifting, fast-ramping and price arbitrage capabilities. In this paper, we propose a stochastic bi-level optimization model to find the optimal nodal storage capacities required to achieve a certain price volatility level in a highly volatile electricity market. The decision on storage capacities is made in the upper level problem and the operation of strategic/regulated generation, storage and transmission players is modeled at the lower level problem using an extended Cournot-based stochastic game. The South Australia (SA) electricity market, which has recently experienced high levels of price volatility, is considered as the case study for the proposed storage allocation framework. Our numerical results indicate that 80% price volatility reduction in SA electricity market can be achieved by installing either 340 MWh regulated storage or 420 MWh strategic storage. In other words, regulated storage firms are more efficient in reducing the price volatility than strategic storage firms.