Q1. Value a call option with strike price $105, expiring in 2 years, where the underlying at time 0 has a sport price of 100. This asset has probability 0.65 to increase 30% relatively in value each year and probability 0.35 to increase only just 5% in relative value. At the same time, the interest rate at time 0 is 1%, this has probability 0.70 to increase 4% in absolute value year on year, or stay the same. Calculate the value of this call option.

Q2. Suppose that the interest rate on a one-year risk-free bonds is 5%, and now a corporate bond is issued with a face value of 1,000, maturing in 1-year. The payoff in the case that the company doesn't default is 1050 with probability 80%, and 20% for the default case where bond holders receive nothing. With this chance in default, investors demand a 3% risk premium, which can be seen priced into the market. (a) What is the price of the bond, and what is its promised yield? (b) What is a recovery rate and how will the price of the bond change with a recovery rate of 40% (c) You are worried about the risk of default on your bond investments. Do you buy or sell credit default swaps?

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