Consider a 3-period interest-rate tree with the following values. i0 = 5% i1L = 4.3% i1H...

Consider a 3-period interest-rate tree with the following values. i0 = 5% i1L = 4.3% i1H = 6.3% i2LL = 4.2% i2HL = 5.7% i2HH = 8.2% In this tree, find the price of

a) A 3-year, annual-pay bond with a coupon of 7.25% using the tree

b) A 3-year, annual-pay bond with a coupon of 7.25% using pathwise valuation

c) A 3-year, annual-pay bond with a coupon of 7.25% that is callable in years 1 and 2 at 101

Solutions

Expert Solution

(A) and (C) are answered in image

(A) The price of a 3-year, annual-pay bond with a coupon of 7.25% using the tree is 105.05

(C) The price of a 3-year, annual-pay bond with a coupon of 7.25% that is callable in years 1 and 2 at 101 is 103.07

(B) There are 4 possible paths for a 3-year bond and each cash flow will be discounted at each respective path-specified rate. The price of A 3-year, annual-pay bond with a coupon of 7.25% using pathwise valuation is 105.7629

Path	Year 1	Year 2	Year 3	Value
1	5%	4.30%	4.20%	108.0909
2	5%	4.30%	5.70%	106.7571
3	5%	6.30%	5.70%	105.152
4	5%	6.30%	8.20%	103.0516
			Average	105.7629

Note: Value of Path 1 = ((7.25/1.05)+(7.25/1.05*1.043)+(107.25/(1.05*1.043*1.042))) = 108.09

Value at path 2 = ((7.25/1.05)+(7.25/1.05*1.043)+(107.25/(1.05*1.043*1.057))) = 106.7571

Value at path 3 = ((7.25/1.05)+(7.25/1.05*1.063)+(107.25/(1.05*1.063*1.057))) = 105.152

Value at path 4 = ((7.25/1.05)+(7.25/1.05*1.063)+(107.25/(1.05*1.063*1.082))) = 103.0516

jeff jeffy answered 1 year ago

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