Seminar Essay

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SEMINARS PART 2 OF THE COURSE CHAPTERS 4-5 1. - Final Exam December 2009 – Question 2: Consider an economy that lasts only one period (two dates: t = 0 and t = 1). In t = 1 three different states of nature may occur: the economy may be in a boom state, the economy may be in a recession state or the economy may be in a crisis state. In this economy 3 assets exist with the following prices and payoffs: Assets Price in t=0 Boom (s=1) Asset 1 Asset 2 Asset 3 140 95 45 200 100 100 Payoffs in t=1 States Recession (s=2) 150 100 50 Crisis (s=3) 100 100 0 a) Show that one of the assets is redundant and that as a result markets are not complete. b) Suppose we add another asset to this market: a call option whose underlying is asset 3, with a strike price K = € 80, which matures in t=1 and with a cost (price or premium) of c0 = € 5. Are markets complete in this case? If they are, then calculate the price of the Arrow-Debreu securities associated with each state of nature. c) What is the no-arbitrage price in t = 0 of a basic bond that matures in t = 1? What is the interest rate associated with that bond? d) What is the no-arbitrage forward price of Asset 1 agreed in t = 0 for delivery in t = 1? e) If a new asset appears in the market that pays 0 in t = 1 if the economy is in a boom state, € 50 if the economy is in a recession state, and 0 if the economy is in a crisis state, what is its no-arbitrage price in t = 0? f) Imagine that the price at which that asset is offered to the market is € 10. Design an arbitrage strategy to benefit from that opportunity (limit yourself to using asset 1, asset 3, the call and the new asset), and define the positions that you would take in each security. 2. - Final Exam September 2010 – Question 2: Consider a call and a put option on a stock with the same strike price. The relevant information is the following: Stock price

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