Dresden 2006 – scientific programme

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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 14: Financial Markets and Risk Management III

AKSOE 14.4: Talk

Thursday, March 30, 2006, 17:30–18:00, BAR 205

Geometric motion in prices, and its limited validity. — •Alessandro Sapio — LEM - Sant’Anna School of Advanced Studies - Piazza Martiri della Liberta’ 33 - 56127 Pisa (Italy)

In research on speculative and commodity market dynamics, log-linear price models have been widely applied (e.g. Geometric Brownian Motion, multiplicative diffusion processes). Yet, recent studies on wholesale power markets cast doubts on the general validity of the log-linear property. Linear models outperform log-linear ones (Lucia and Schwartz, 2001, Review of Derivative Research), and the returns volatility goes like the inverse of price (Bottazzi, Sapio and Secchi, 2005, Physica A).

This paper explores the limits to application of log-linear price models, and contributes with new insights on risk measurement and derivative pricing in markets with different institutional and technological features.

Spot pricing equations implied by periodic and continuous double auction settings are specified, and some conditions behind linear and log-linear price fluctuations are deduced. Geometric Motion emerges when individual orders are shaped by past prices (e.g. through forecasting rules, or as purchasing costs). This may not occur in power markets: trading is only based on current revenues and costs, because of non-storability.

Results are compared with predictions based on an alternative view - the efficient markets hypothesis - and the merits of the suggested framework are discussed.