Pricing and hedging Asian options under Levy processes and robust long-term investing with learning about stock returns

In this work we propose a parametric model using the techniques of time-changed subordination that captures the implied volatility smile. We demonstrate that the Fourier-Cosine method can be used in a semi-static way to hedge for quadratic, VaR and AVaR risk. We also observe that investors looking to hedge VaR can simply hold the amount in a portfolio of mostly cash, whereas an investor hedging AVaR will need to hold more risky assets. We also extend ES risk to a robust framework. A conditional calibration method to calibrate the bivariate model is proposed. For a robust long-term investor who maximizes their recursive utility and learns about the stock returns, as the willingness to substitute over time increases, the equity demand decreases and consumption-wealth ratio increases. As the preference for robustness increases the demand for risk decreases. For a positive correlation, we observe that learning about returns encourages the investor to short the bond at all levels of u and vice versa

Pricing and hedging Asian options under Levy processes and robust long-term investing with learning about stock returns

In this work we propose a parametric model using the techniques of time-changed subordination that captures the implied volatility smile. We demonstrate that the Fourier-Cosine method can be used in a semi-static way to hedge for quadratic, VaR and AVaR risk. We also observe that investors looking to hedge VaR can simply hold the amount in a portfolio of mostly cash, whereas an investor hedging AVaR will need to hold more risky assets. We also extend ES risk to a robust framework. A conditional calibration method to calibrate the bivariate model is proposed. For a robust long-term investor who maximizes their recursive utility and learns about the stock returns, as the willingness to substitute over time increases, the equity demand decreases and consumption-wealth ratio increases. As the preference for robustness increases the demand for risk decreases. For a positive correlation, we observe that learning about returns encourages the investor to short the bond at all levels of u and vice versa

Eliciting Risk Preferences and Elasticity of Substitution

Risk aversion and elasticity of intertemporal substitution (EIS) are separated via the celebrated recursive utility building on certainty equivalents of indirect utility. Based on an alternative separation method, we formulate a questionnaire for simultaneous and consistent estimation of risk aversion, subjective discount rate, and EIS. From a representative group of 1,153 respondents, we estimate parameters for these preferences and their variability within the population. Risk aversion and the subjective discount rate are found to be in the orders of 2 and 0, respectively, not diverging far away from results from other studies. Our estimate of EIS in the order of 10 is larger than often reported. Background variables like age and income have little predictive power for the three estimates. Only gender has a significant influence on risk aversion in the usually perceived direction that females are more risk-averse than males. Using individual estimates of preference parameters, we find covariance between preferences toward risk and EIS. We present the background reasoning on objectives, the questionnaire, a statistical analysis of the results, and economic interpretations of these, including relations to the literature.