second derivative test Archives - Infinity is Really Big

February 20, 2019February 21, 2019

New Video: Immunization, Part 5

Redington immunization is a concept that can be defined in terms of derivatives of present value functions.

Given asset cashflows $A_{0},A_{1},A_{2},\ldots,A_{n}$ and liability cashflows $L_{0},L_{1},L_{2},\ldots,L_{n},$ each set of flows occurring at times $t=0,1,2,\ldots,n,$ the expressions $P_{A}(i)=\displaystyle\sum_{t=0}^{n}A_{t}(1+i)^{-t}$ and $P_{L}(i)=\displaystyle\sum_{t=0}^{n}L_{t}(1+i)^{-t}$ represent the present values of these cashflows, as functions of an arbitrary periodic interest rate $i.$

If we let $h(i)=P_{A}(i)-P_{L}(i)=\displaystyle\sum_{t=0}^{n}C_{t}(1+i)^{-t},$ where $C_{t}=A_{t}-L_{t},$ then we say the liabilities are Redington immunized … Read the rest

February 12, 2019February 12, 2019

New Video: Immunization, Part 4

In “New Video: Immunization, Part 3“, I showed that if a liability cashflow is not immunized by an asset cashflow, we might be able to make modifications to change this state of affairs.

In particular, the time of payment of one of the asset amounts could be changed to achieve, at least, Redington immunization. To be even … Read the rest