Heterogeneity in risk preferences leads to stochastic volatility. (English) Zbl 1416.91397
Summary: This paper studies the price processes of a claim on terminal endowment and of a claim on firm book value when the underlying variables follow a bivariate geometric Brownian motion. If the state-price process is multiplicatively separable into time and endowment functions, our main result shows that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, the endowment function is not a power function. In a pure exchange economy populated by two agents with constant relative risk aversion (CRRA) preferences we confirm the separability, and we show furthermore that firm (endowment) price volatility is stochastic (state-dependent) if, and only if, both agents are heterogeneous in risk-preferences.
MSC:
| 91G50 | Corporate finance (dividends, real options, etc.) |
| 60J70 | Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) |
| 35Q91 | PDEs in connection with game theory, economics, social and behavioral sciences |
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