Now, consider the following one-period model, with two assets and three possible outcomes: Price at time 0 Price at time 1 Outcome Outcome 2 Outcome 3 Asset 1 55 40 60 88 Asset 2 85 60 120 96 There is also a bank account that pays an interest rate R = 0.2 per period. (b) Write down the set of simultaneous equations that must be satisfied by the risk-neutral probabilities (91, 92 and 93) for this market. (You may assume that such probabilities do indeed exist in this case.)

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Chapter1: Making Economics Decisions
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Now, consider the following one-period model, with two assets and three possible outcomes:
Price at time 0
Price at time 1
Outcome 1 Outcome 2 Outcome 3
Asset 1
Asset 2
55
40
60
88
85
60
120
96
There is also a bank account that pays an interest rate R=0.2 per period.
(b) Write down the set of simultaneous equations that must be satisfied by the risk-neutral
probabilities (q1, q2 and qs) for this market. (You may assume that such probabilities do indeed
exist in this case.)
(c) Solve this set of simultaneous equations to determine q1, 92
and
(d) Are there any arbitrage opportunities in this market? Justify your answer.
(e) Is this market complete? Again, justify your answer.
Transcribed Image Text:Now, consider the following one-period model, with two assets and three possible outcomes: Price at time 0 Price at time 1 Outcome 1 Outcome 2 Outcome 3 Asset 1 Asset 2 55 40 60 88 85 60 120 96 There is also a bank account that pays an interest rate R=0.2 per period. (b) Write down the set of simultaneous equations that must be satisfied by the risk-neutral probabilities (q1, q2 and qs) for this market. (You may assume that such probabilities do indeed exist in this case.) (c) Solve this set of simultaneous equations to determine q1, 92 and (d) Are there any arbitrage opportunities in this market? Justify your answer. (e) Is this market complete? Again, justify your answer.
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