| Abstract: |
| This is joint work with Carey Caginalp. The relationship between price volatility and a market
extremum is examined via stochastic differential equations using a fundamental economics model of supply and
demand.
By examining randomness through a microeconomic setting, we obtain the implications of randomness in the
supply and demand, rather than assuming that price has randomness on an empirical basis. Within a very
general setting the volatility has a minimum at price extrema. The maximum of volatility occurs when
prices are changing most rapidly. A key issue is that randomness arises from the supply and demand,
and the variance in the stochastic differential equation governing the logarithm of price must reflect this.
Analogous results are obtained by further assuming that the supply and demand are dependent on the
deviation from fundamental value of the asset. The supply/demand approach also shows that fat tails (in
particular x^(-2) falloff) are endogenous to the trading mechanism. |
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