the bank's declining sales of structured products to private customers, more specifically so-called bank savings with equity returns and guaranteed minimum amounts. You suggest that the return on the savings product can alternatively be linked to something most people are more interested in. You propose a savings product that after 1.5 years gives a 20% return if Rosenborg wins one series gold during the period, and a 140% return if Rosenburg wins two series golds. If Rosenborg does not win league gold during period, the buyer of the savings product receives the deposit amount back after 1.5 years. The deposit amount for one share is USD 10,000. Your friend thinks this is an exciting idea, but is wondering how the product to be valued. You tell her that there is an efficient market for buying and sale of derivatives that pay out depending on whether Rosenborg wins the series or not. In this market there are three derivative contracts: Contract A: Pays 100 USD in 1.5 years if Rosenborg wins one series gold in 1.5 years, and otherwise. Contract B: Pays 100 USD in 1.5 years if Rosenborg wins two series gold in 1.5 years, and otherwise. Contract C: Pays out USD 100 in 0.5 years if Rosenborg wins one series gold during 0.5 years, and otherwise. Suppose in 0.5 years we know whether Rosenborg will win league gold or not in the first year. In 1.5 years, we will know whether Rosenborg will win league gold or not the second year. The market prices of derivative contracts today are (to 3 decimal places): Contract A: USD 16,010. Contract B: USD 1,884. . Contract C: USD 9,802. a) Show how you can use (some of) the contracts above, as well as risk-free investment, to replicate the cash flows of a share in the savings product. Assume that you can borrow in and out at a risk-free, continuous interest rate of 4%. Find the value of the savings product. b) Use derivative contracts A, B and C to find risk neutral (risk adjusted) probabilities that Rosenborg will win league gold in the first year, the second year given victory the first year, and the second year given no victory the first year. the bank's declining sales of structured products to private customers, more specifically so-called bank savings with equity returns and guaranteed minimum amounts. You suggest that the return on the savings product can alternatively be linked to something most people are more interested in. You propose a savings product that after 1.5 years gives a 20% return if Rosenborg wins one series gold during the period, and a 140% return if Rosenburg wins two series golds. If Rosenborg does not win league gold during period, the buyer of the savings product receives the deposit amount back after 1.5 years. The deposit amount for one share is USD 10,000. Your friend thinks this is an exciting idea, but is wondering how the product to be valued. You tell her that there is an efficient market for buying and sale of derivatives that pay out depending on whether Rosenborg wins the series or not. In this market there are three derivative contracts: Contract A: Pays 100 USD in 1.5 years if Rosenborg wins one series gold in 1.5 years, and otherwise. Contract B: Pays 100 USD in 1.5 years if Rosenborg wins two series gold in 1.5 years, and otherwise. Contract C: Pays out USD 100 in 0.5 years if Rosenborg wins one series gold during 0.5 years, and otherwise. Suppose in 0.5 years we know whether Rosenborg will win league gold or not in the first year. In 1.5 years, we will know whether Rosenborg will win league gold or not the second year. The market prices of derivative contracts today are (to 3 decimal places): Contract A: USD 16,010. Contract B: USD 1,884. . Contract C: USD 9,802. a) Show how you can use (some of) the contracts above, as well as risk-free investment, to replicate the cash flows of a share in the savings product. Assume that you can borrow in and out at a risk-free, continuous interest rate of 4%. Find the value of the savings product. b) Use derivative contracts A, B and C to find risk neutral (risk adjusted) probabilities that Rosenborg will win league gold in the first year, the second year given victory the first year, and the second year given no victory the first year
