Implied liquidity risk premia in option markets

The theory of conic finance replaces the classical one-price model by a two-price model by determining bid and ask prices for future terminal cash flows in a consistent manner. In this framework, we derive closed-form solutions for bid and ask prices of plain vanilla European options, when the density of the log-returns is log-concave. Assuming that log-returns are normally or Laplace distributed, we apply the results to a time-series of real market data and compute an implied liquidity risk premium to describe the bid–ask spread. We compare this approach to the classical attempt of describing the spread by quoting Black–Scholes implied bid and ask volatilities and demonstrate that the new approach characterize liquidity over time significantly better.