Upper and Lower Bounds of Put and Call Option Value: Stochastic Dominance Approach

Applying stochastic dominance rules with borrowing and lending at the risk-free interest rate, we derive upper and lower values for an option price for all unconstrained utility functions and alternatively for concave utility functions. The derivation of these bounds is quite general and fits any kind of stock price distribution as long as it is characterized by a “nonnegative beta.” Transaction costs and taxes can be easily incorporated in the model presented here since investors are not required to revise their portfolios continuously. The “price” that is paid for this generalization is that a range of values rather than a unique value is obtained.