Detecting and Measuring Nonlinearity
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 t...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-08-01
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| Series: | Econometrics |
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| Online Access: | http://www.mdpi.com/2225-1146/6/3/37 |
| _version_ | 1811262386151096320 |
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| author | Rachidi Kotchoni |
| author_facet | Rachidi Kotchoni |
| author_sort | Rachidi Kotchoni |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T19:24:28Z |
| format | Article |
| id | doaj.art-e1d37744d45f4fbbadaa14dc5a9794aa |
| institution | Directory Open Access Journal |
| issn | 2225-1146 |
| language | English |
| last_indexed | 2024-04-12T19:24:28Z |
| publishDate | 2018-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Econometrics |
| spelling | doaj.art-e1d37744d45f4fbbadaa14dc5a9794aa2022-12-22T03:19:31ZengMDPI AGEconometrics2225-11462018-08-01633710.3390/econometrics6030037econometrics6030037Detecting and Measuring NonlinearityRachidi Kotchoni0EconomiX-CNRS (UMR7235), Bureau G-517, Université Paris Nanterre, 92000 Nanterre, FranceThis 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.http://www.mdpi.com/2225-1146/6/3/37conditional expectationnonlinearityorthogonal polynomialsreturn-risk trade-off |
| spellingShingle | Rachidi Kotchoni Detecting and Measuring Nonlinearity Econometrics conditional expectation nonlinearity orthogonal polynomials return-risk trade-off |
| title | Detecting and Measuring Nonlinearity |
| title_full | Detecting and Measuring Nonlinearity |
| title_fullStr | Detecting and Measuring Nonlinearity |
| title_full_unstemmed | Detecting and Measuring Nonlinearity |
| title_short | Detecting and Measuring Nonlinearity |
| title_sort | detecting and measuring nonlinearity |
| topic | conditional expectation nonlinearity orthogonal polynomials return-risk trade-off |
| url | http://www.mdpi.com/2225-1146/6/3/37 |
| work_keys_str_mv | AT rachidikotchoni detectingandmeasuringnonlinearity |