Detecting and Measuring Nonlinearity

Rachidi Kotchoni

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Abstract: 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 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

Published in Econometrics, 2018, 6 (3), ⟨10.3390/econometrics6030037⟩

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Journal Article: Detecting and Measuring Nonlinearity (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02435765

DOI: 10.3390/econometrics6030037

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