Electricity markets are significantly more volatile than other comparable financial or commodity markets. Extreme price outcomes and their transmission between regions pose significant risks for market participants. We examine the dependence between extreme spot price outcomes in the Australian National Electricity Market (NEM). We investigate extremal dependence both in a univariate and multivariate setting, applying the extremogram developed by Davis and Mikosch (2009) and Davis et al. (2011Davis et al. ( , 2012. We measure the persistence of extreme prices within individual regional markets and the transmission of extreme prices across different regions. With both 5-minute and 30minute price data, we find that extreme prices are more persistent in the market with a higher share of intermittent renewable energy. We also find that persistence of extreme prices is more prevalent in more concentrated markets. We also show significant extremal price dependence between different regions, which is typically stronger between physically interconnected markets. The dependence structure of extreme prices shows asymmetric and time-dependent patterns. Applying the extremograms, we further show the effectiveness of the Australian Energy Market Commission's 2016 rebidding rule with respect to reducing the share of isolated price spikes that are often considered as an indication of strategic bidding. Our results provide important information for hedging decisions of market participants and for policy makers who aim to reduce market volatility and extreme price outcomes through effective regulations which guide the trading behaviour of market participants as well as improved network interconnections.