This study proposes a direct estimation method for recovering subjective probability distributions from option prices. We find that the subjective cumulative distribution function and subjective statistics are represented as static portfolios composed of plain vanilla options. The portfolio...

This paper proposes a general method to recover the subjective probability distribution of nonlinear payoffs from option prices. We show that the characteristic function of the distribution can be represented as the present value of a static option portfolio with complex-valued portfolio...