Forward Contracts

The thing about math at a certain level is that there are no more easy exercises.  I have learned to make a habit of creating simple exercises.  These are for the forward price, which is the contracted price to buy an asset at time T in the future; and the prepaid forward price, which is the price paid now for an asset that will be delivered at time T.  In these problems, r is the continuous interest rate, and delta is the continuous dividend rate.
F^P_{0, T} = S_o = S_o -PV(divs) = S_0 e^{-\delta} T
F_{0, T} = S_0 e^{rT} = S_oE^{rT} - AV(divs) = S_0e^{(r-\delta)}T

  1. S_0 =1000, r=0.04, \delta = 0.01\quad F^P_{0, 6m}?
  2. S_0 =800, r=0.02, \delta = 0\quad F_{0, 2m}?
  3. S_0 =800, r=0.02, \delta = 0\quad F^P_{0, 2yr}?
  4. S_0 =500, r=0.04, \delta = 0\quad F_{0, 2yr}?
  5. S_0 =500, r=0.04, \delta = 0\quad F_{0, 6m}?
  6. S_0 =500, r=0.04, \delta = 0\quad F^P_{0, 1yr}?
  7. S_0 =100, r=0.03, \delta = 0.01\quad F^P_{0, 2yr}?
  8. S_0 =100, r=0.03, \delta = 0.01\quad F^P_{0, 3m}?
  9. S_0 =1000, r=0.04, \delta = 0.01\quad F_{0, 1yr}?
  10. S_0 =1000, r=0.04, \delta = 0.01\quad F_{0, 6m}?
  11. S_0 =800, r=0.02, \delta = 0\quad F^P_{0, 5m}?
  12. S_0 =100, r=0.03, \delta = 0.01\quad F_{0, 1yr}?
  13. S_0 =100, r=0.03, \delta = 0.01\quad F_{0, 9m}?
  14. S_0 =500, r=0.04, \delta = 0\quad F^P_{0, 9m}?
  15. S_0 =1000, r=0.04, \delta = 0.01\quad F^P_{0, 1yr}?
  16. S_0 =800, r=0.02, \delta = 0\quad F_{0, 1yr}?

Solutions:

  1. 1000e^{-0.01*0.5}=995.01
  2. 800e^{0.02*(\frac 1 6)}=802.67
  3. 800
  4. 500e^{.04*2}=541.64
  5. 500e^{0.04*.5}=510.10
  6. 500
  7. 100e^{-0.01 *2}=98.02
  8. 100e^{-0.01*0.25}=99.75
  9. 1000e^{0.04-0.01}=1030.45
  10. 1000e^{(0.04-0.01)*0.5} =1015.11
  11. 800
  12. 100e^{0.03-0.01}=102.02
  13. 100e^{(0.03-0.01)*0.75}=101.51
  14. 500
  15. 1000e^{-0.01}=990.05
  16. 800e^{0.02}=816.16

Later today, I will post some tougher ones that require a little thinking.

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