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1.What is the current fair value of the four-year collared floater if the risk-neutral probabilities in the binomial tree are 0.5 and 0.5 for the up and down moves, respectively.

*Interest rates expressed as annualized rates A collared floater is like a variable rate bond, but with an upper limit and a lower limit on the rate of coupon payment. Consider, for example, annual rates coupon payment and one-year spot interest rates. In the following table, the current one-year spot interest rate is denoted by r in column (1). Depending on the current spot interest rate, the collared floater with a face value of 662.5 dollars will pay the holder of this floater a sum a year later, as given in column (2) of the table. The binomial tree below gives the evolution of one-year spot interest rates over a four year period. 1. What is the current fair value of the four-year collared floater if the risk-neutral probabilities in the binomial tree are 0.5 and 0.5 for the up and down moves, respectively? Current Rate, r (1) r 8% Collared Floater with face value 662.5 pays at the end of the year (2) 33.12 662.5 x r% 53 10.50 % 8.75% 6.2% 4.5% 9.50% 6.00% 5.2% 6.25% 5.50% 4.75%