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Solution 7

# Solution 7 - Fin 448 Fixed-Income Securities Homework...

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Fin 448: Fixed-Income Securities Homework Solution 7 Wei Yang 1 Risk-neutral pricing (1.1) 800 = 900 π * 1 + 60(1 - π * 1 ) π * 1 = 0 . 880952 900 = 1000 π * 2 + 120(1 - π * 2 ) π * 2 = 0 . 886364 (1.2) The senior bond gets \$100 at the end of year 2, no matter which state realizes. With a 0 risk-free rate, the price of the bond at the end of year 1 is also \$100 under no bankruptcy. At the end of year 1 if the firm goes bankrupt, the senior bond gets \$60. Hence, the price of the bond today is 100 π * 1 + 60(1 - π * 1 ) = 95 . 2381 (1.3) At the end of year 2 when assets value is \$1000, the junior bond gets \$100; when assets value is \$120, it gets \$20. The price of the junior bond at the end of year 1 is 100 π * 2 + 20(1 - π * 2 ) = 90 . 9091 At the end of year 1 if the firm goes bankrupt, the junior bond gets 0. Hence, the price of the junior bond today is 90 . 9091 π * 1 + 0(1 - π * 1 ) = 80 . 0866 (1.4) At the end of year 2, the value of the stocks is \$800, so the price is \$80 per share. At the end of year 1, 900 - 100 - 90 . 9091 100 = 7 . 09091 Finally, the stock price today is 800 - 95 . 2381 - 80 . 0866 100 = 6 . 24675 1

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2 Corporate bond (2.1) s = π * D L * = 5% × 40% = 2% (2.2)
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