Detecting and Measuring Nonlinearity

Econometrics 2018, 6(3), 37

27 Pages Posted: 6 Jan 2021

See all articles by Rachidi Kotchoni

Rachidi Kotchoni

Université Paris Nanterre; African Development Bank

Date Written: 2018


This paper proposes an approach to measure the extent of nonlinearity of the exposure of a financial asset to a given risk factor. The proposed measure exploits the decomposition of a conditional expectation into its linear and nonlinear components. We illustrate the method with the measurement of the degree of nonlinearity of a European style option with respect to the underlying asset. Next, we use the method to identify the empirical patterns of the return-risk trade-off on the SP500. The results are strongly supportive of a nonlinear relationship between expected return and expected volatility. The data seem to be driven by two regimes: one regime with a positive return-risk trade-off and one with a negative trade-off.

Keywords: conditional expectation; nonlinearity; orthogonal polynomials; return-risk trade-off

JEL Classification: C10, G10

Suggested Citation

Kotchoni, Rachidi, Detecting and Measuring Nonlinearity (2018). Econometrics 2018, 6(3), 37, Available at SSRN:

Rachidi Kotchoni (Contact Author)

Université Paris Nanterre ( email )

200 Avenue de la République
Nanterre, Hauts de Seine 92000

African Development Bank ( email )

Rue Joseph Anoma
Abidjan, Ivory Coast 01 BP 1387
Ivory Coast (Cote D'ivoire)

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