1) Consider an elementary market model

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1) Consider an elementary market model. Assume that there exist a stock and a cash bond in the model. The initial price of the stock is £40. The investor believes that with probability 2/3 the stock price will rise to £60 and with probability 1/3 the stock price will rise to £80 at the end of the time period. The cash bond has an initial price of £l and it will with certainty deliver £7/4 at the end of the period. Does this model admit any arbitrage opportunities? Explain your answer. Write payoffs for a digital call option with a maturity at the end of the time period and a strike price of £70. Use the replication principle and find a price of this contingent claim. Interpret the solution to the problem using obtained values for x and o. Find the price using the risk neutral valuation formula. Discuss the equivalence of the two approaches. The quality of your answer is very important for the mark. Please explain your answer carefully, explain the notation you use, give clear references to definitions, theorems and claims that you use to support your statements.