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One of the evident consequences of the deregulation in electricity industry is the volatility of market clearing prices (MCP). In this paper, we use variance to measure this price volatility and propose supply function equilibria and Cournot models to characterize the impact of bilateral contracts on the variance of MCP. As the result, we show that bilateral contracts reduce the variance of MCP. Finally, a numerical study based on Singapore electricity market to support our models is presented.