inclusive have the following common conditions

Question

Inclusive have the following common conditions:

• the riskless interest rate r > 0 ;
• the underlier is trading at a spot price S ; and
• all options are European vanillas on the same underlier and have the same maturity date T ≥ 0.

Question 1

What are the no-arbitrage boundary conditions for the value of a European vanilla Call option with strike price K₁ ?

Question 2

Another European vanilla Call option with strike price K ₂ > K₁ is trading in the market. What are the new no-arbitrage boundary conditions for the value of the European vanilla Call option with strike price K₁?

Question 3

Another European vanilla Call option with strike price K₃ is trading in the market. At the expiry of the three options (i.e. at T = 0 ), what are the new no-arbitrage boundary conditions for the value of the European vanilla Call option with strike price K₁ , if K ₃ < K₁ < K₂ and K₁ - K ₃ = K ₂ - K₁ ?