What is it about?
When the randomness of a derivative price is fully spanned by the randomness of the underlying asset price the market is said to be complete. In this case, absence of arbitrage opportunities is enough to ensure a unique price of the derivative. However, in general this is not the case and absence of arbitrage opportunities only provides an interval of feasible derivative prices. We use portfolio theory to single out one particular derivative price and show that this price results in equilibrium.
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Why is it important?
A portfolio manager can always increase his Sharpe ratio by adding a derivative, priced with a non-zero premium for the unspanned risk, to his portfolio.
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This page is a summary of: Kelly trading and option pricing, Journal of Futures Markets, May 2021, Wiley,
DOI: 10.1002/fut.22210.
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