Valuing life insurance products with the Option Interpolation Model (OIM). Life insurance products are often characterized by embedded options and guarantees. The value of these options and guarantees depends heavily on the prevailing economic conditions. Examples are the interest rate in case of profit-sharing options or the return on investments in case of Unit-Linked products with a return guarantee. The value of embedded options and guarantees is an integral part of the market value of insurance liabilities. A correct and consistent valuation is therefore essential. Not only from the perspective of good risk management, but also for internal and supervisory reporting.

## Own Risk and Solvency Assessment (ORSA)

Under Solvency II it is not sufficient to calculate the current market value of embedded options and guarantees only. Insurers are required, at least once a year, to generate projections of the development of the solvency ratio and the related risks within the Own Risk and Solvency Assessment (ORSA). The value of options and guarantees is a fundamental part of this prospective analysis, primarily due to the sensitivity of these products to future economic and market developments. Besides using a consistent valuation for the various Solvency II applications, it is also important to include the value of the options and guarantees consistently across other forward-looking applications of the insurer, such as Asset Liability Management (ALM) and ex-ante risk monitoring.

Steps to be taken

## Ortec Finance Option Interpolation Model (OIM)

In practice, determining the current market value of the options and guarantees is usually not a problem. But calculating this value in forward-looking ORSA, ALM, and monitoring applications is computationally very challenging as one needs to assess the option value for each year in each scenario. The most commonly-applied solution is to use an approximating function. A well-known example of such a technique is Least Squares Monte Carlo (LSMC). At Ortec Finance however, we favor an alternative approach, which we call the Option Interpolation Model (OIM).

Step 4: Use the OIM for density forecasts

## The OIM process involves four steps:

1. Specify the (economic and/or non-economic) risk drivers of the option or guarantee at hand
2. Obtain option values from the embedded value system based on pre-sampled risk driver values
3. Calibrate and validate the function
4. Use the OIM in forward-looking projections

## Difference between LSMC and OIM methods

The main difference between LSMC and OIM is that LSMC is based on a large number of inaccurate option values, whereas OIM works with a much smaller number of true or accurate values. By making a smart selection from the possible future values for the relevant risk drivers, one avoids having to perform many thousands of valuations. We have developed advanced techniques to select the risk driver values to be used in the process. In the end this makes it possible to determine an accurate and consistent value for the options and guarantees for all reporting applications.

## Key takeaways from the Option Interpolation Model:

• Consistency between internal valuation tools used for reporting and the ORSA, ALM and monitoring projections
• Easy to calibrate and superior replication of sensitivities of liabilities, even in the tails
• Excellent performance even with a large number of stochastic scenarios