Which of the following inequalities correctly states the relationship between the difference in the prices of two European calls that differ only by exercise price A)(X_2? - X₁)(1 + r)^-T ≥ C_e(S₀,T,X₁)- C_e(S₀,T,X₂) B)(X_2? - X₁)≥ C_e(S₀,T,X₂)- C_e(S₀,T,X₁) C)(X₂ - X₁)(1 + r)^-T ≥ C_e(S₀,T,X₁)+ C_e(S₀,T,X₂) D)(X_2? - X₁)≥ C_e(S₀,T,X₁)- C_e(S₀,T,X₂) E)none of the above

Question

Quizplus · Accepted Answer

The difference in the prices of two European calls that differ only by exercise price is given by the difference in their payoffs at expiration. The payoff of a European call option is given by max(S_T - X, 0), where S_T is the stock price at expiration and X is the exercise price. Therefore, the difference in the payoffs of two European call options with different exercise prices is given by max(S_T - X₁, 0) - max(S_T - X₂, 0). This difference is always positive, since S_T - X₁ ≥ S_T - X₂. Therefore, the difference in the prices of two European calls that differ only by exercise price is also always positive.

Which of the Following Inequalities Correctly States the Relationship Between