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and Forwards on Currencies (Page 5558) F S e r r Tf0 0? ?( )Options, Futures, and Other Derivatives, 5th edition 169。 2021 by John C. Hull Futures on Consumption Assets (Page 59) F0 ? S0 e(r+u )T where u is the storage cost per unit time as a percent of the asset value. Alternatively, F0 ? (S0+U )erT where U is the present value of the storage costs. Options, Futures, and Other Derivatives, 5th edition 169。 2021 by John C. Hull The Cost of Carry (Page 60) ? The cost of carry, c, is the storage cost plus the interest costs less the ine earned ? For an investment asset F0 = S0ecT ? For a consumption asset F0 ? S0ecT ? The convenience yield on the consumption asset, y, is defined so that F0 = S0 e(c–y )T Options, Futures, and Other Derivatives, 5th edition 169。 2021 by John C. Hull Futures Prices amp。 Expected Future Spot Prices (Page 61) ? Suppose k is the expected return required by investors on an asset ? We can invest F0e–r T now to get ST back at maturity of the futures contract ? This shows that F0 = E (ST )e(r–k )T Options, Futures, and Other Derivatives, 5th edition 169。 2021 by John C. Hull Futures Prices amp。 Future Spot Prices (continued) ? If the asset has –no systematic risk, then k = r and F0 is an unbiased estimate of ST –positive systematic risk, then k r and F0 E (ST ) –negative systematic risk, then k r and F0 E (ST )