One of the Deficiencies of the Bootstrap Method Is That $d ( t )$

Multiple Choice

One of the deficiencies of the bootstrap method is that it only returns discount functions that are on discrete dates. One approach to address this problem for cashflows that do not fall on these dates is to split them into allocations to near dates for which discount functions are available. Suppose we have discount functions $d ( t )$ , where $d ( 1 ) = 0.95$ and $d ( 2 ) = 0.90$ . Assuming continuous compounding, how will a cashflow at $t = 1.5$ years of $100 be allocated to $t = 1$ and $t = 2$ years such that the present value and duration of cashflow remains the same? Assume that the forward rate between 1 and 2 years is constant. The allocation of cashflows is:

A) $48.63 at one year and $51.33 at two years.
B) $47.33 at one year and $52.63 at two years.
C) $46.19 at one year and $53.87 at two years.
D) $50 at one year and $50 at two years.