Fin 441 Homework 4

FIN 441

Homework 4

Mingyu Yang

1.a)i) Balance of marginal account change = 4000 - 2000 = 2000 loss

      ii) price per kilogram = 2000/5000 = 0.40 loss

    b) price per kilogram = current price - change in price = 1.50 - 0.40 = 1.10

    c)i) balance of amrgin account change = 4000 + 2000 = 6000

       ii) price per kilogram = 2000/5000 = 0.40

    d) price per kilogram = current price + change in price = 1.50 + 0.40 = 1.90

2. S0 = 950   r = 7%   dividend yield = 2%    T = 4/12

     F = S0 x e^((r-d)T)

         = 950 x e^((7%-2%)*⅓)

     Futures price = 965.9660

     futures contract = 950 x 250 = 237,500

3.a)  S = 40   d = 3  r = 10% T1 = 12/12   T2 = (12-8)/12

        forward price = Se^rT1 - de^rT2 = 40e^0.1 - 3e^0.1*⅓  = 41.1052

   b)i) S` = 45  T` = 6/12

         forward price = 45e^0.1*½ - 3e^0.1*⅓ = 44.2055

         change in forward price = 44.2055 - 41.1052 = 3.1003

      ii) The value of the initial forward contract is the difference between the beginning value and the ending value of the stock price with the discounted risk free rate.

      iii) value of the initial forward contract = (FT(t) - FT(0))*e^-r*(T-t)

           = (49 -  40e^0.1 - 3e^0.1*⅓) x e^-0.1(1-½)

           = (49 - 41.1052) x e^-0.1(1-½)

           = 7.5098

4.a) storage cost = (0.36/12)e^(0.12*1/12) + (0.36/12)e^(0.12*2/12) + (0.36/12)e^(0.12*3/12)

                            = 0.03e^(0.12*1/12) + 0.03e^(0.12*1/6) + 0.03e^(0.12*1/4)

                            = 0.0303 + 0.0306 + 0.0309

                            = 0.0918

   b) accured interest = 12 x (e^0.12*3/12 - 1) = 0.3655