Embedded options and interest rate risk for insurance companies,banks and other financial institutions

We explore how embedded options in assets and liabilities of financial institutions impact interest rate risk, which is measured by equity value change with interest rate movements. We find that both asset and liability durations decline when embedded options are present where liability duration declines more substantially. This leads to a duration-mismatch and a negative change in equity value when interest rates rise, but a positive change for interest rate declines. In a more sophisticated model, an option adjusted duration-matching strategy eliminates interest rate risk caused by duration-mismatch, but the convexity-mismatch remains large due to large negative convexity of callable assets and large positive convexity of putable liabilities. The interest rate risk introduced by convexity mismatch is quite large in comparison to that of duration mismatch. The pattern of this impact is complex and strongest for roughly intermediate maturities. We propose and show that a simple convexity hedging strategy with putable assets and callable liabilities (or caps and floors combined with floating rate assets and liabilities) reduces the interest rate risk substantially.