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Distributional Risk, Stochastic Volatility and Precautionary Savings

Suen, Richard M. H. (2016): Distributional Risk, Stochastic Volatility and Precautionary Savings.

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This paper analyses the optimal saving behaviour of a risk-averse and prudent consumer who faces two sources of income risk: risk as described by a given probability distribution and risk in the distribution itself. The latter is captured by the randomness in the parameters underlying the probability distribution and is referred to as distributional risk. Stochastic volatility, which generally refers to the randomness in the variance, can be viewed as a form of distributional risk. Necessary and sufficient conditions by which an increase in distributional risk will induce the consumer to save more are derived under two specifications of preferences: expected utility preferences and Selden/Kreps-Porteus preferences. The connection (or lack of) between these conditions and stochastic volatility is addressed. The additional conditions under which a prudent consumer will save more under greater volatility risk are identified.

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