One of the early examples of stochastic volatility models is Clark [1973]. He suggested that asset price movements should be tied to the rate at which transactions occur. To accomplish this, he made a distinction between transaction time and calendar time. This framework has hitherto been...

We develop a conditional capital asset pricing model in continuous-time that allows for stochastic beta exposure. When beta co-moves with market variance and the stochastic discount factor (SDF), beta risk is priced, and the expected return on a stock deviates from the security market line. The...