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 $50. The investor believes that with probability 1/3 the stock price will rise to $60 and with probability 2/3 the stock price will rise to $80 at the end of the time period. The cash bond has an initial price of $1 and it will with certainty deliver $7/5 at the end of the period. Does this model admit any arbitrage opportunities? Explain your answer. Use the replication principle and find a price of a digital call option with a maturity at the end of the time period and a strike price of $70. Interpret obtained values for I and p. Find the price using risk neutral valuation formula. Prove the equivalence of the two approaches. 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 $50. The investor believes that with probability 1/3 the stock price will rise to $60 and with probability 2/3 the stock price will rise to $80 at the end of the time period. The cash bond has an initial price of $1 and it will with certainty deliver $7/5 at the end of the period. Does this model admit any arbitrage opportunities? Explain your answer. Use the replication principle and find a price of a digital call option with a maturity at the end of the time period and a strike price of $70. Interpret obtained values for I and p. Find the price using risk neutral valuation formula. Prove the equivalence of the two approaches