{'fraction_non_alphanumeric': 0.025069637883008356, 'fraction_numerical': 0.0, 'mean_word_length': 4.991666666666666, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A MEAN VALUE-AT-RISK FRAMEWORK FOR SPECULATING AND HEDGING WITH OPTIONS

We construct a mean value-at-risk (VaR) framework for speculating and hedging with options, similar to the Markowitz mean-variance portfolio model. The choice of the optimal option strategy depends on market expectations, risk aversion, and tail estimates, and does not depend on the cost of the option. The optimal speculative strategy can be achieved at a high risk, which not only entails betting on the right side of the market, but also determining the optimal exercise price. The model can also be extended to a risk hedging framework, and can be generalized to accommodate more complex derivative instruments and parameter specifications.