Subjective Probability Distributions of Nonlinear Payoffs : Recovering Option Payoff and Agent's Utility Distributions

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 weights. By applying Fourier inversion, we derive the subjective probability distribution from the characteristic function. As an illustration, we successfully recover the subjective probability distributions of option payoffs and agent's utility. Additionally, we elucidate the theoretical relation between expected option returns and the pricing kernel, offering enhanced insights compared to previous studies. This research contributes a valuable framework for understanding subjective probability distributions and their implications for financial analysis and decision-making