# Fixed Income (Bonds With Embedded Options) question

Could someone please help me with this question page 336, reading 54, #5D I understand the first couple steps. For example: 98.994 = 108.5/1.09603 100.591 = 108.5/1.07862 101.938 = 108.5/1.06437 – That’s as far as I can go. How do we compute: 99.826? How do we compute: 102.638? Finally, how do we compute the value of the option free bond to be 102.076? ~~ Thanks in advance for any responses.

Curriculum or Schweser?

Ok, Found it in curriculum: Since you’ve arrived at Year 2 Values: 98.994 = 108.5/1.09603 100.591 = 108.5/1.07862 101.938 = 108.5/1.06437 Lets get them back at Year 1 Values: There are 2 nodes in Year 1: Upper and Lower node. Upper Node (Year 1): The value of the UPPER NODE in Year 1 will be determined using the average of Node 1 (\$98.994) and Node 2 (\$100.591) in Year 2. So, [(\$98.994+\$8.5)/1.08481 + (\$100.591+\$8.5)/1.08481] / 2 = \$99.826 Lower Node (Year 2): The value of the LOWER NODE in Year 1 will be determined using the average of Node 2 (\$100.591) and Node 3 (\$101.938) in Year 2. So, [(\$100.591+\$8.5)/1.06944 + (\$101.938+\$8.5)/1.06944] / 2 = \$102.638 So, we have the year 1 nodes: Upper Node: \$99.826 Lower Node: \$102.638 Using the average of these nodes in year 1, we’ll get back to Year 0 (Today). So, [(\$99.826+\$8.5)/1.075 + (\$102.638+\$8.5)/1.075] / 2 = \$102.076 Hope that helps That really helps. Now I can figure the question out and move on. Thank you VERY much for taking the time and writing the complete answer. I have no idea why textbook does not write a complete answer to these binomial trees.

You’re welcome Do agree with the fact that textbooks need to have complete answers (with calculations) though!