Discretely Rebalanced Option Hedge with Fixed Marginal Transaction Cost and Resolution to Implied Volatility Smile

2011 ◽  
Author(s):  
Chen Guo
Keyword(s):  
Transaction Cost ◽  
Implied Volatility ◽  
Volatility Smile

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

2021 ◽  
Author(s):  
Andrew Na
Keyword(s):  
Stock Returns ◽  
Implied Volatility ◽  
Calibration Method ◽  
Recursive Utility ◽  
Asian Options ◽  
Volatility Smile ◽  
Bivariate Model ◽  
Risky Assets ◽  
Fourier Cosine

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

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