Let ={w1,w2,w3,w4},F=2,P[{i}]>0 for all i=1,,4 and T=2 (time to maturity). Suppose the isky stock price is described as follows: S01=5,S11(w1)=S11(w2)=8,S11(w3)=S11(w4)=4 and S21(w1)=9, S21(w2)=S21(w3)=6,S21(w4)=3. Suppose we work with the natural filtration of S1,F=(FtS1)t=0,1,21. 1. Represent all possible paths of S1 on a tree. 3 pts 2. Say the riskless asset is given by St0=(1+r)t. Determine RNA:{rR : an EMM for X1= S1/S0 exists }. For each rRNA find the set of EMMs for X1, denoted by Pr. Determine Pr, i.e., the size of Pr. 3. For r/RNA find an arbitrage opportunity. 7 pts 4. Fix rRNA, and, using (S0,S1), determine the replicating strategy for the pay-off C described by C(w1)=c1,C(w2)=c2,C(w3)=c3 and C4=c4, where ci are positive constants. Determine the initial cost of this strategy and then compare it with EQ[C/S20] for each QPr. 10pts Let ={w1,w2,w3,w4},F=2,P[{i}]>0 for all i=1,,4 and T=2 (time to maturity). Suppose the isky stock price is described as follows: S01=5,S11(w1)=S11(w2)=8,S11(w3)=S11(w4)=4 and S21(w1)=9, S21(w2)=S21(w3)=6,S21(w4)=3. Suppose we work with the natural filtration of S1,F=(FtS1)t=0,1,21. 1. Represent all possible paths of S1 on a tree. 3 pts 2. Say the riskless asset is given by St0=(1+r)t. Determine RNA:{rR : an EMM for X1= S1/S0 exists }. For each rRNA find the set of EMMs for X1, denoted by Pr. Determine Pr, i.e., the size of Pr. 3. For r/RNA find an arbitrage opportunity. 7 pts 4. Fix rRNA, and, using (S0,S1), determine the replicating strategy for the pay-off C described by C(w1)=c1,C(w2)=c2,C(w3)=c3 and C4=c4, where ci are positive constants. Determine the initial cost of this strategy and then compare it with EQ[C/S20] for each QPr. 10pts