For each of the pairs of a and b in table choose the most

Question

For Questions assume all options are European style with maturity T.A'K call' is call option with strike price K. A 'knockout' option has payout zero if the defined event occurs.

Ordering option prices by monotonicity theorem I

Consider the following eight options I-VIII. Here, K_1 2 3.

I K₁ call

II K₁ call that knocks out if S_T > K₂

III K₁ call that knocks out if S_t > K₂ for any 0 ≤ t ≤ T

IV K₁ call that knocks out if S_T 1

V K₁ call that knocks out if S_t 1 for any 0 ≤ t ≤ T

VI K₁, K₂ call spread (long one K₁ call, short one K₂ call)

VII Digital call with strike K₁ and payout K₂ - K₁

VIII K₁, K₂, K₃ call ladder (long one K₁ call, short one K₂ call, short one K₃ call)

For each of the pairs of A and B in Table, choose the most appropriate relationship between prices at time t ≤ T out of =, ≥, ≤ and ?, where ? means the relationship is indeterminate.