How do market makers and sophisticated investors/traders determine option value? In his July 2019 essay entitled “Trading Volatility”, Emanuel Derman outlines the history and shortcomings of option valuation as described by the Black-Scholes model, which estimates the value of an option on an asset as a function of the asset’s price and volatility. He also addresses extensions of this model. Based on mathematical derivations and his knowledge of option markets, he concludes that:
- The Black-Scholes model builds upon assumptions that do not match empirical evidence (for example, stock prices follow a Brownian process with known volatility).
- Empirically, asset options exhibit volatility expectations that vary across strike prices (an implied volatility “smile”), with each asset having a unique smile. Elaborate extensions of the Black-Scholes model attempt to account for smiles, but none of the extensions is widely accepted as a replacement for the base model.
- In practice, option market makers typically hedge against, or bet on, changes in future volatility. Their counterparts (retail investors) typically bet on stock price changes.
- There is likely no correct model of markets and options, because investor/trader behavior continuously adapts to changes in market behavior and new technologies.
In summary, option models are not, and likely never will be, good enough to squeeze the expiration risk out of asset options.
See also the summary of his book, My Life as a Quant: Reflections on Physics and Finance.
