Question

(A) ATX stock is expected to pay dividend of AUD 1 per share in three months and AUD 1.50 per share in five months. The ATX stock price is AUD 55 and the risk-free interest is 8% per annum with continuous compounding for all maturities and Mr. Brown has taken a short position in a six-month forward contract.

(i) What is the initial value of the forward contract?

(ii) What is the forward price of this forward contract

(B) Three months later, the price of the ATX stock is AUD 50 and the risk-free interest rate is still 8% per annum

(i) What is the value of the short position in the forward contract?

(ii) What is the forward price of this forward contract?

Answer 1

Answer (A-(i)):

The initial value of Forward Contract is:

Initially the value of forward contract is set to be Zero, it is assumed that the value at the time of initiaition is zero becuase the amount which one party wil have to pay to another party is in the future and not deriving value at the time of their agreement which means no money has been exchanged at the begining of the contract.

F = S / d(0,T)

The above expression, where (F) is equal to the forward price, (S) is the current spot price of the underlying asset, and d(0,T) is the discount factor for the time variable between the initial date and the delivery date. The discount factor depends on the length of the forward contract. Mathematically, this is demonstrated as an equilibrium price because any forward price above or below this value represents an arbitrage opportunity, Hence At a date where (T) is equal to zero, the value of the forward contract is also zero.

Answer (A-(ii)):

The forward price of Forward Contract is: