University of Isfahan Journal of Asset Management and Financing 2383-1189 Articles in Press 2026 06 02 Nonlinear and Asymmetric Dynamics of Implied Risk and Abnormal Stock Return: Evidence from Put Options in the Tehran Stock Exchange Using Quantile-on-Quantile Approach Nonlinear and Asymmetric Dynamics of Implied Risk and Abnormal Stock Return: Evidence from Put Options in the Tehran Stock Exchange Using Quantile-on-Quantile Approach 30456 10.22108/amf.2026.148390.2039 FA Sayyede Elnaz Afzaliyan Boroujeni Department of Management, Na.C., Islamic Azad University, Najafabad, Iran. Abdolmajid Abdolbaghi Department of Management, Faculty of Industrial Engineering and Management, Shahrood University of Technology, Shahrood, Iran. Sayyede Leila Afzaliyan Boroujeni Department of Financial Management, Faculty of Management and Accounting, Farabi Colleges, University of Tehran, Qom, Iran Naser Khani Department of Management, Na.C., Islamic Azad University, Najafabad, Iran. Journal Article 2026 02 17 This research aims to examine the nonlinear and asymmetric dynamics of abnormal stock return(AR) in facing the implied risk extracted from put options(IV), its changes(ΔIV), idiosyncratic volatility(IDVOL), and historical volatility of the stock(STD) in Tehran Stock Exchange, and seeks to, by passing linear and mean based approaches, identify the conditional and heterogeneous dependencies of the risk–return relationship at various market levels. The research, using data of put options and underlying stocks during the period 2016–2024, has been conducted. Abnormal stock return were calculated through the market model, and the variables of IV, ΔIV, IDVOL, and STD were computed and used as the main variables of the research. For analyzing the nonlinear and distribution dependent relationships between volatility variables and AR, the quantile on quantile regression was applied, which makes possible the simultaneous examination of quantiles of dependent and explanatory variables. The findings showed that the effect of volatilities on AR depends on the market conditions and different levels of return distribution; such that the effect of volatility variables is mostly significant and prominent in the tails of return distribution, i.e., in conditions of severe recession or notable boom, while it weakens in the middle levels of return distribution, indicating that the sensitivity of AR to risk depends more on the prevailing market conditions than on the magnitude of volatility. The set of this evidence indicates that the mean based models and even conventional quantile regressions are not able to fully reflect the behavioral and structural heterogeneity existing in the market. This research aims to examine the nonlinear and asymmetric dynamics of abnormal stock return(AR) in facing the implied risk extracted from put options(IV), its changes(ΔIV), idiosyncratic volatility(IDVOL), and historical volatility of the stock(STD) in Tehran Stock Exchange, and seeks to, by passing linear and mean based approaches, identify the conditional and heterogeneous dependencies of the risk–return relationship at various market levels. The research, using data of put options and underlying stocks during the period 2016–2024, has been conducted. Abnormal stock return were calculated through the market model, and the variables of IV, ΔIV, IDVOL, and STD were computed and used as the main variables of the research. For analyzing the nonlinear and distribution dependent relationships between volatility variables and AR, the quantile on quantile regression was applied, which makes possible the simultaneous examination of quantiles of dependent and explanatory variables. The findings showed that the effect of volatilities on AR depends on the market conditions and different levels of return distribution; such that the effect of volatility variables is mostly significant and prominent in the tails of return distribution, i.e., in conditions of severe recession or notable boom, while it weakens in the middle levels of return distribution, indicating that the sensitivity of AR to risk depends more on the prevailing market conditions than on the magnitude of volatility. The set of this evidence indicates that the mean based models and even conventional quantile regressions are not able to fully reflect the behavioral and structural heterogeneity existing in the market.