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The authors consider the problem of simulating the times of events such as extremes and barrier crossings in diffusion processes. They develop a rejection sampler based on Shepp [Shepp, Journal of Applied Probability 1979; 16:423–427] for simulating an extreme of a Brownian motion and use it in a general recursive scheme for more complex simulations, including simultaneous simulation of the minimum and maximum and application to more general diffusions. They price exotic options that are difficult to price analytically: a knock‐out barrier option with a modified payoff function, a lookback option that includes discounting at the risk‐free interest rate, and a chooser option where the choice is made at the time of a barrier crossing. The Canadian Journal of Statistics 38: 738–755; 2010 © 2010 Statistical Society of Canada