Options Portfolio Selection
23 Pages Posted: 28 Nov 2017 Last revised: 19 Sep 2018
Date Written: November 23, 2017
We develop a new method to optimize portfolios of options in a market where European calls and puts are available with many exercise prices for each of several potentially correlated underlying assets. We identify the combination of asset-specific option payoffs that maximizes the Sharpe ratio of the overall portfolio: such payoffs are the unique solution to a system of integral equations, which reduce to a linear matrix equation under suitable representations of the underlying probabilities. Even when implied volatilities are all higher than historical volatilities, it can be optimal to sell options on some assets while buying options on others, as hedging demand outweighs demand for asset-specific returns.
Keywords: options, portfolio choice, Sharpe ratio, duality, multiple assets
JEL Classification: G11, G12
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