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Futures

VIEWS: 2 PAGES: 6

									                                             Introduction



Options et marchés spéculatifs

               Futures: illustrations
               Professor André Farber

               The three worksheets in this file illustrate the calculation of:
               - equilibrium futures/forward prices
               - futures/forward contract valuation
               - arbitrage

               StIndFut1 illustrates discrete dividends
               StIndFut2 illustrates continuous dividends
               FwdCur    illustrates forward/futures on currencies




                                               Page 1
                  c29f8fe1-1001-40f7-bac9-a41ce0f212f2.xls StIndFut1


Stock index futures - Illustration
Discrete dividends
Currency:                                      Euro
Maturity of futures (months)                     12
Underlying index of futures contract:     DJStoxx50
Value of one point of index:                    10 Euro
Current value of underlying index            3,650
"Value" of underlying asset                  36,500 Euro
Dividend yield (if continuous)               0.00%
Next dividends (if discrete)                Amount Mat.(months)
                                               100            6

Interest rate (cont.)                        3.00%

Futures prices calculation
Present value of future dividend              98.51
Adjusted price                             3,551.49
Futures price                              3,659.65

Arbitrage : illustration
Delivery price                         3,000.00
Value of futures contract                 640.15
Type of arbitrage                  Reverse cash and carry

                                                           Now      Maturity
Index                              Sell                 3650.00       -S(T)
Future value of dividends                                           -101.51
Borrow/Lend                        Invest               -3650.00    3761.16
Futures                            Buy                         0   -3000.00 S(T)
Total                                                          0     659.65
PV(future profit)                                         640.15
c29f8fe1-1001-40f7-bac9-a41ce0f212f2.xls StIndFut1




      Type = 1
                                          StIndFut2


Stock index futures-illustration
Constant continuous dividend yield

Currency                                 USD
Maturity of futures (months)                3
Underlying index                     S&P 500
Value of one point of index               250 USD
Current index                       1,310.00
"Value" of underlying asset        327,500.00 USD
Dividend yield                         2.00%
Interest rate (cont.)                  5.00%

Futures price                        1,319.86 =S * exp((r-q)(T-t)


Valuation : illustration
Suppose delivery price =             1,330.00
Value of futures contract               -10.01 =S*exp(-q(T-t))-K*exp(-r(T-t))

Arbitrage : illustration

Type of arbitrage              Cash and carry
                                                Quantity        Cash flows
                                                                      t        T
Index                          Buy               0.995012     -1303.47     -S(T)
Bor/Lend bef                   Borrow                   1      1303.47 -1319.86
Futures                        Sell                     1            0 1330.00 +S(T)
Total                                                                0     10.14

PV(future profit)                                     10.01




                                           Page 4
            StIndFut2




Type = -1




             Page 5
                   c29f8fe1-1001-40f7-bac9-a41ce0f212f2.xls FwdCur


Forward/Futures contract on a currency
Spot exchange rate               1.050 Euro/USD
Time to maturity                    0.5
Price BEF Tbil               0.980199 IntRate         4.00% (continuous)
Price USD Tbil               0.970446 IntRate         6.00% (continuous)

Forward exchange rate           1.040 =Spot*B$/Beuro
                                1.040 =Spot * exp((reuro-r$)(T-t))

Arbitrage : illustration
Delivery price                     1.02            Type = 1
Type of arbitrage           Reverse cash and carry
USD Tbill                   Sell           1.02      -S(T)
Bor/Lend bef                Invest        -1.02       1.04
Forward                     Buy               0       S(T) -1.02
Total                                         0       0.02

Valuation : illustration
Three month later
Maturity                        0.250
Spot exchange rate              1.060
IntRate bef                     0.040
IntRate USD                     0.050

Value of underlying asset       1.047
PV(Exercice price)              1.029
Value of forward contract       0.018

New forward exch.rate F1        1.057
F1 - F0                         0.018
PV(F1-F0)                       0.018




                                        Page 6

								
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