Aloulou-Ellouze (2017) Does Fundamental Value Run Asset Price Formation Process?

Summary

Tests whether fundamental value or trader evaluations govern asset price formation using daily S&P TSX 60 options (Canada, Jan 2012–Dec 2013). Extracts risk-neutral densities (RNDs) nonparametrically via Nadaraya-Watson kernel regression on the implied-volatility surface (Aït-Sahalia-Lo 2000), constructing constant-maturity (30-day) option prices without Black-Scholes distributional bias. A bivariate vector autoregression (VAR$(2)$) on forecast errors and a switching proxy (relative change in RND homogeneity) finds bidirectional Granger causality: past forecast errors drive strategy switching, and switching reduces future forecast errors — supporting the Keynes "beauty contest" view that heterogeneous trader evaluations, not fundamental deviations, govern price formation.

Key Claims

• Average forecast error is $-0.32\%$: prices slightly overshoot fundamental predictions on average.
• Forecast error $\mathrm{FE}_t = (E_t[P] - P_{t+1})/E_t[P]$; switching $\mathrm{SW}_t$ = relative change in risk-neutral density homogeneity (proxy for strategy migration between fundamentalists and chartists).
• Both $\mathrm{FE}$ and $\mathrm{SW}$ are stationary (Augmented Dickey-Fuller (ADF) confirmed); bivariate VAR$(2)$ selected by information criteria.
• Bidirectional Granger causality: $C_{(2,1)} > 0$ (past forecast errors increase switching); $C_{(1,3)} < 0$, $t = -5.10$ (past switching reduces future forecast errors).
• Heterogeneous agents model: fundamentalists forecast $\tilde{P}^a_{t+1} - P_t = a(F_t - P_t)$; chartists forecast $\tilde{P}^a_{t+1} - P_t = b(P_t - P_{t-1})$; market price $P_{t+1} = c\bigl[p_t \tilde{P}^a_{\text{fund}} + (1-p_t)\tilde{P}^a_{\text{chart}}\bigr] + F_t$; weights shift toward better-performing group (evolutionary switching).
• Nonparametric RND extraction avoids Black-Scholes distributional assumptions; constant-maturity prices interpolated along the implied-volatility surface (Aït-Sahalia-Lo 2000).

Concepts Introduced or Extended

• Black-Scholes Option Pricing — nonparametric alternative for risk-neutral density extraction via Nadaraya-Watson kernel regression (Aït-Sahalia-Lo 2000); option prices used as information content about trader expectations without imposing lognormal return distribution

Entities Mentioned

• Abderrahmen Aloulou
• Siwar Ellouze

Quotes

"The price formation process appears governed by trader evaluations and strategy migration rather than deviation of prices from fundamental value."

My Take

The methodological contribution — nonparametric Nadaraya-Watson RND extraction to avoid Black-Scholes bias — is sound and well-motivated. The VAR results are clean ($C_{(1,3)}$, $t = -5.10$ is strong). The main limitation is the switching proxy: relative change in RND homogeneity is an indirect and potentially noisy measure of actual strategy migration. The dataset is short (2 years, single index, Canada only), limiting generalizability. The "beauty contest" conclusion is intuitive but depends on accepting the switching proxy's validity as a measure of heterogeneous agent behavior.