Prove the following bounds on European call options C(S, t), on an underlying share price S, with no dividends:

(a) C_A ≥ C_B, where C_A and C_B are calls with the same exercise price E and expiry dates T_A and T_B respectively, and TA > TB.

(b)

 

where C₁,C₂ and C₃ are calls with the same expiry T, and have exercise prices E₁, E₂ and E₃ respectively, where E₁ < E₂ < E₃.

Consider E₂ = λE₁ + (1 − λ)E₃.

Transcribed Image Text:

E3 - E2 c. E2 - E, C2 Ез — Е1 Ез — Е1