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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).