10. In the general single period market model with = {W1, W2, W3}, one risky asset, S, and a money market account, we have So = 4 for the risky asset. Moreover, the effective rate of interest on the money market account is 5% and at time t = 1 we have W1 W2 W3 S₁ 100 50 40 21 21 21 (a) Calculate all risk-neutral probability measures for this model. [4 Marks] (b) State if the model is arbitrage-free. Give a brief reason for your answer. [2 Marks] (c) A large bank has designed an investment product with payoff X at time t = 1. Given W₁ W2 W3 X 0 1 1.5 show that X is an attainable contingent claim. [4 marks]

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A movie studio wishes to determine the relationship between the revenue generated from the streaming of comedies and the revenue generated from the theatrical release of such movies. The studio has the following bivariate data from a sample of fifteen comedies released over the past five years. These data give the revenue x from theatrical release (in millions of dollars) and the revenue y from streaming (in millions of dollars) for each of the fifteen movies. The data are displayed in the Figure 1 scatter plot. Theater revenue, x Streaming revenue, y (in millions of (in millions of dollars) dollars) 13.2 10.3 62.6 10.4 20.8 5.1 36.7 13.3 44.6 7.2 65.9 10.3 49.4 15.7 31.5 4.5 14.6 2.5 26.0 8.8 28.1 11.5 26.1 7.7 28.2 2.8 60.7 16.4 6.7 1.9 Streaming revenue (in millions of dollars) 18+ 16+ 14 12+ xx 10+ 8+ 6+ 2- 0 10 20 30 40 50 60 70 Theater revenue (in millions of dollars) Figure 1 Send data to calculator Send data to Excel The least-squares regression line for these data has a slope…