On bid and ask pricing of European options via direct discretization of Choquet distorted expectations

We present a numerical approach to compute bid and ask prices of European options within the conic finance paradigm. In particular, we show how discretizing option bid and ask pricing formulae, where the latter are expressed in terms of Choquet integrals, allows to perform efficient pricing and calibration by means of the COS method and the fast Fourier transform technique. Additionally, the approach introduced provides alternative expressions for risk-neutral European option prices by leveraging the relationship between Choquet and Riemann-Stieltjes integrals. These alternative formulations, requiring only the discretization of the cumulative distribution function of the (transformed) terminal value of the underlying asset, enhance computational efficiency under risk-neutral settings. We provide practical illustrations of the methodology when the underlying asset process follows Heston or Variance Gamma dynamics for both pricing and implied liquidity calculations.