Stochastic discount factor

Summary

The concept of the stochastic discount factor (SDF) is used in financial economics and mathematical finance. The name derives from the price of an asset being computable by "discounting" the future cash flow \tilde{x}_i by the stochastic factor \tilde{m}, and then taking the expectation. This definition is of fundamental importance in asset pricing. If there are n assets with initial prices p_1, \ldots, p_n at the beginning of a period and payoffs \tilde{x}_1, \ldots, \tilde{x}_n at the end of the period (all xs are random (stochastic) variables), then SDF is any random variable \tilde{m} satisfying :E(\tilde{m}\tilde{x}_i) = p_i, \text{for } i=1,\ldots,n. The stochastic discount factor is sometimes referred to as the pricing kernel as, if the expectation E(\tilde{m},\tilde{x}_i) is written as an integral, then \tilde{m} can be interpreted as the kernel function in an integral t

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