Question: Let t 1 What is E St St 98
Let 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?
Answer to relevant QuestionsLet KT = S0erT. Compute Pr(St KT ) for a variety of T s from 0.25 to 25 years. How do the probabilities behave? How do you reconcile your answer with the fact that both call and put prices increase with time? Suppose 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)? Assume S0 = $100, r = 0.05, σ = 0.25, δ = 0, and T = 1. Use Monte Carlo valuation to compute the price of a claim that pays $1 if ST > $100, and 0 otherwise. (This is called a cash-or-nothing call and will be further ...Suppose that x1∼ N(0, 1) and x2 ∼ N(0.7, 3). Compute 2000 random draws of ex1 and ex2. a. What are the means of ex1 and ex2? Why? b. Create a graph that displays a frequency distribution in each case. Suppose that the processes for S1 and S2 are given by these two equations: dS1= α1S1dt + σ1S1dZ1 dS2 = α2S2dt + σ2S2dZ2 dQ = αQQdt + Q_ η1dZ1+ η2dZ2 Show that, to avoid arbitrage,
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