# bff5040tute-11answer - T10Q1(a Because K = 100 so payoffs...

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T10Q1 (a) Because K = 100, so payoffs of call at maturity are: C u = max{ u S − K, 0} = 10 and C d =max{d S −K,0}=0. Initial cost of the portfolio would be: ΔS + B = 100Δ + B, since the portfolio is replicated consisting of Δ units of the stock and borrowing/ investment of \$B. If the call is replicated by the portfolio, it would be Δ (u S ) +exp(r)B = Cu, Δ (d S )+rB = C d Derived from above formulas, it would be 110Δ+exp(0.05)B = 10, 90Δ+exp(0.05)B = 0 which indicates Δ = 1/2 and B = −42.8, i.e., this portfolio has a long position in a half unit of the stock and a borrowing of 42.8. Therefore, the cost is (1/2)100−42.8 = 7.2. Because the portfolio replicates the call, so cost of call also has to be 7.2. (b) p (1.10) + (1 − p)(0.90) = exp(0.05), so p = 0.756. The expected value of the call payoffs is: 0.756*(10) + 0.244*(0) = 7.56. Then, 7.56/exp(0.05) = 7.2. (c) The put has zero value, Pu = 0 if the stock price goes up, and Pd = 10 if the
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