  Models for spin systems known from statistical physics are applied by analogy
in econometrics in the form of agent-based models. Researchers suggest that the
state variable temperature $T$ corresponds to volatility $\sigma$ in capital
market theory problems. To the best of our knowledge, this has not yet been
theoretically derived, for example, for an ideal agent system. In the present
paper, we derive the exact algebraic relation between $T$ and $\sigma$ for an
ideal agent system and discuss implications and limitations.
