Finance (Derivative Securities) ASSIGNMENT [15 marks] Questions 1-3 inclusive have the following common conditions (unless stated otherwise): the riskless interest rate r > 0 ; the underlier is...

Finance (Derivative Securities)



ASSIGNMENT [15 marks]

Questions 1-3 inclusive have the following common conditions (unless stated otherwise):

• 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

[4 marks]

What are the no-arbitrage boundary conditions for the value of a European vanilla Call option with strike price
K
₁
?

Question 2

[5 marks]

Another European vanilla Call option with strike price
K
₂
>
K
₁
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
K
₁?

Question 3

[6 marks]

Another European vanilla Call option with strike price
K
₃
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
K
₁
, if
K
₃
K
₁
K
₂
and
K
₁
-
K
₃
=
K
₂
-
K
₁
?



Finance (Derivative Securities) ASSIGNMENT [15 marks] Questions 1-3 inclusive have the following common conditions (unless stated otherwise): 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 [4 marks] What are the no-arbitrage boundary conditions for the value of a European vanilla Call option with strike price K1 ? Question 2 [5 marks] 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 [6 marks] 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 ? page 1 k2="" and="" k1="" −="" k="" 3="K" 2="" −="" k1="" page="">