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Q&A Bank Part 3 - Question 3.5 (v)

B

barbados

Member
Hi,

I can derive the tree for using the first numeraire. However, for the second numeraire I can't get the correct numbers. For example, how to derive the number 9.05 using the second numeraire. I am expecting something like:

Discount factor x [0.5382 x 19 - 0.4618 x 1]. But what is used for the discount factor then. If I use exp{-0.05} I won't get the correct number.

Hope someone can help on this part of the question.

Thanks.
 
The discounting/accumulating for the N terms comes straight from the tree for Y. (We can't use the 5% number you suggest as that comes from the tree for X.)

So to get the 9.05 using Numeraire Y we need:

V(1,up)=1.0637 [19 x 0.5382 / 1.1450 - 1 x 0.4618 / 1.0858] = 9.05

So the discounting is different for each path, which highlights the benefit of using a cash bond as the numeraire: the discounting can come outside the expectation because it is non-path-dependent.

This is really the most important point to take away from this question.
 
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