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1. Consider a financial market with two assets over the time interval [0,T]. Trading can take place at n+1 discrete time points to, ..., tn where ti = iA, i 0, 1, ..., n, and A=T is the time distance between trading times. The first asset is risk- free with interest rate era > 0 per time period. The second asset is a stock whose price in period i (= 1,..., n) is given by Sia = S(-1)A exp (a + Bui), where a and B are coefficients and vi, i 1,.., n, are i.i.d. with P(Vi = -1) = P1, P(vi = 0) = P2, P(V; = 1) = P3. Here, pi + p2 +p3 = 1. (a) [5 pts) Suppose you know that p = P3. How would you estimate the two parameters a and using observed stock prices, Sia, i = 1, ..., n? 1. Consider a financial market with two assets over the time interval [0,T]. Trading can take place at n+1 discrete time points to, ..., tn where ti = iA, i 0, 1, ..., n, and A=T is the time distance between trading times. The first asset is risk- free with interest rate era > 0 per time period. The second asset is a stock whose price in period i (= 1,..., n) is given by Sia = S(-1)A exp (a + Bui), where a and B are coefficients and vi, i 1,.., n, are i.i.d. with P(Vi = -1) = P1, P(vi = 0) = P2, P(V; = 1) = P3. Here, pi + p2 +p3 = 1. (a) [5 pts) Suppose you know that p = P3. How would you estimate the two parameters a and using observed stock prices, Sia, i = 1, ..., n

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