This paper, authored by Robert C. Merton and published in October 1971, delves into the theory of rational option pricing. The author argues that despite the simplicity of options as contingent-claim assets, their pricing remains a complex issue due to the lack of a unified theory. The paper aims to derive theorems about the properties of option prices based on weak assumptions to gain universal support. It begins by laying the foundational assumptions for a rational theory of option pricing, emphasizing that options should not be dominant or dominated securities. The paper then examines the Black and Scholes (B-S) model in detail, showing that their formula is valid under weaker assumptions than those originally proposed. It derives several extensions to the B-S theory and discusses the effects of dividends and changing exercise prices on option valuation. The analysis shows that dividends and unfavorable exercise price changes are the primary reasons for premature exercising, which is the only rational reason for American options to sell at a premium over European options. The paper also explores the rational pricing of put options, noting that the value of a put option is determined by the price of a call option. It derives a formula for the European put option price and discusses the challenges of valuing American put options due to the possibility of early exercise. Finally, the paper presents an alternative derivation of the B-S model, showing that it can be derived under weaker assumptions and including the possibility of stochastic interest rates. The derived formula is shown to be identical to the B-S formula in the special case of a constant interest rate and log-normally distributed stock prices. The paper concludes by discussing the implications of the derived formula for empirical testing and applications.This paper, authored by Robert C. Merton and published in October 1971, delves into the theory of rational option pricing. The author argues that despite the simplicity of options as contingent-claim assets, their pricing remains a complex issue due to the lack of a unified theory. The paper aims to derive theorems about the properties of option prices based on weak assumptions to gain universal support. It begins by laying the foundational assumptions for a rational theory of option pricing, emphasizing that options should not be dominant or dominated securities. The paper then examines the Black and Scholes (B-S) model in detail, showing that their formula is valid under weaker assumptions than those originally proposed. It derives several extensions to the B-S theory and discusses the effects of dividends and changing exercise prices on option valuation. The analysis shows that dividends and unfavorable exercise price changes are the primary reasons for premature exercising, which is the only rational reason for American options to sell at a premium over European options. The paper also explores the rational pricing of put options, noting that the value of a put option is determined by the price of a call option. It derives a formula for the European put option price and discusses the challenges of valuing American put options due to the possibility of early exercise. Finally, the paper presents an alternative derivation of the B-S model, showing that it can be derived under weaker assumptions and including the possibility of stochastic interest rates. The derived formula is shown to be identical to the B-S formula in the special case of a constant interest rate and log-normally distributed stock prices. The paper concludes by discussing the implications of the derived formula for empirical testing and applications.