A Generalization of the Brennan‐Rubinstein Approach for the Pricing of Derivatives
在离散时间经济中推导出无偏好的期权定价方程，资产收益服从连续分布，为Black-Scholes模型提供新充分条件，并得到标的资产具有变换正态分布（如负偏态对数正态）时的欧式期权解析解。
ABSTRACT This paper derives preference‐free option pricing equations in a discrete time economy where asset returns have continuous distributions. There is a representative agent who has risk preferences with an exponential representation. Aggregate wealth and the underlying asset price have transformed normal distributions which may or may not belong to the same family of distributions. Those pricing results are particularly valuable (a) to show new sufficient conditions for existing risk‐neutral option pricing equations (e.g., the Black‐Scholes model), and (b) to obtain new analytical solutions for the price of European‐style contingent claims when the underlying asset has a transformed normal distribution (e.g., a negatively skew lognormal distribution).