Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Frequently a company wants to match its assets and liabilities. However, perfect matching is not practical due to fluctuations in interest rates. So they hedge their risk using immunization. This can be achieved using present value matching, duration matching, and greater convexity for assets. In particular:

  • $PV_{A}(i_0) = PV_{L}(i_0)$
  • $\frac{d}{di} PV_{A}(i)|_{i_0} = \frac{d}{di} PV_{L}(i)|_{i_0}$
  • $\frac{d^2}{di^2} PV_{A}(i)|_{i_0} > \frac{d^2}{di^2} PV_{L}|_{i_0}$

Could we add any extra conditions so that the risk is reduced even more(e.g. could be look at $\frac{d^3}{di^3} PV_{A}(i)$ etc..)?

share|cite|improve this question
You are likely to get some answers on the sister StackExchange site devoted to Quantitative Finance: – Andrey Rekalo May 10 '11 at 23:19

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.