What is Pr(St < $98) for t = 1? How does this probability change when you change t?
Answer to relevant QuestionsLet t = 1. What is E(St |St < $98)? What is E(St |St < $120)? How do both expectations change when you vary t from 0.05 to 5? Let σ = 0.1. Does either answer change? How? Suppose x1∼ N(2, 0.5) and x2 ∼ N(8, 14). The correlation between x1 and x2 is −0.3. What is the distribution of x1+ x2? What is the distribution of x1− x2? For stocks 1 and 2, S1 = $40, S2 = $100, and the return correlation is 0.45. Let r = 0.08, σ1= 0.30, σ2 = 0.50, and δ1= δ2 = 0. Generate 1000 1-month prices for the two stocks. For each stock, compute the mean and ...Let ui ∼ U (0, 1). Compute _12 i=1 ui − 6, 1000 times. (This will use 12,000 random numbers.) Construct a histogram and compare it to a theoretical standard normal density. What are the mean and standard deviation? (This ...The formula for an infinitely lived call is given in equation (12.18). Suppose that S follows equation (20.20), with α replaced by r, and that E* (dV ) = rV dt. Use Itˆo’s Lemma to verify that the value of the call, V ...
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