# The continuously compounded risk free interest rate

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Consider a two-period binomial model with time-steps of size one year each. The continuously compounded risk-free interest rate is 7% per year. In the absence of dividends, the stock price S evolves as follows: 33 . 8 ր 26 ր ց 20 23 . 4 ց ր 18 ց 16 . 2 where u = 1 . 3 and d = 0 . 9. A company sells structured products with a maturity T = 2 years for which an initial investment of \$1000 yields a payoff given by 1000 max parenleftbigg 1 , 1 + k parenleftbigg S T S 0 1 parenrightbigg parenrightbigg at maturity, where S T is the value of the stock at time T and k > 0. (a) Assume stockholders receive a discrete dividend at the end of the first year equal to 6% of the cum-dividend price. Find the market value (that is the no-arbitrage price) of the financial product as a function of k . (b) Which value of k gives a fairly priced contract (that is, is the initial investment of \$1000 equal to the no-arbitrage price of this derivative contract)? Explain your answer.

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6 of 8 3. [3 points] Assume a one-period model securities market model with two assets S 1 and S 2 . The prices at time 0 and at time 1 are respectively given by:
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