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Detecting and Measuring Nonlinearity

EconomiX-CNRS (UMR7235), Bureau G-517, Université Paris Nanterre, 92000 Nanterre, France
Econometrics 2018, 6(3), 37; https://doi.org/10.3390/econometrics6030037
Received: 28 January 2018 / Revised: 18 March 2018 / Accepted: 2 August 2018 / Published: 9 August 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. View Full-Text
Keywords: conditional expectation; nonlinearity; orthogonal polynomials; return-risk trade-off conditional expectation; nonlinearity; orthogonal polynomials; return-risk trade-off
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Kotchoni, R. Detecting and Measuring Nonlinearity. Econometrics 2018, 6, 37.

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