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Question 6.8: Suppose the interest rate r is constant. Given S(0), find th...

Suppose the interest rate r is constant. Given S(0), find the price S(1) of the stock after one day such that the marking to market of futures with delivery in 3 months is zero on that day.

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Let t = 1/365, T = 1/4. We apply the formula (6.11) to get

f(t, T)=S(t)e^{r(T−t)}                (6.11)

f(t, T) − f(0, T) = S(t)e^{r(T−t)} + S(0)e^{rT} = 0

if S(t) = S(0)e^{rt}, that is, if the stock grows at the risk-free rate.

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