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?
Answer to relevant QuestionsSuppose x1∼ N(1, 5), x2 ∼ N(2, 3), and x3 ∼ N(2.5, 7), with correlations ρ1, 2 = 0.3, ρ1, 3 = 0.1, and ρ2,3 = 0.4. What is the distribution of x1+ x2 + x3? x1+ (3× x2) + x3? x1+ x2 + (0.5× x3)? Let ui ∼ U(0, 1). Draw 1000 random ui and construct a histogram of the results. What are the mean and standard deviation? Refer to Figure 19.2. a. Verify that the price of a European put option is $0.0564. b. Verify that the price of an American put option is $0.1144. Be sure to allow for the possibility of exercise at time 0. Assume that the market index is 100. Show that if the expected return on the market is 15%, the dividend yield is zero, and volatility is 20%, then the probability of the index falling below 95 over a 1-day horizon is ...Use Itˆo’s Lemma to evaluate dS−1. For the following four problems, use Itˆo’s Lemma to determine the process followed by the specified equation, assuming that S(t) follows (a) Arithmetic Brownian motion, equation ...
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