Valuation of embedded option in Asset and Liability Management

The financial crisis of the beginning of the millennium and the recent crisis have led many pension funds to adopt different management approach to overcome the arising difficulties to maintain a solid financial status. Among these, the adoption of an indexation policy which is now conditional on the solvability of the fund have been widely adopted. Pension funds recognizing conditional inflation indexation targets are obliged to pay an additional payoff that is linked to the inflation rate through some specific rule. The additional payoff normally takes the form of a contingent claim conditional to a “measure” of sustainability of the payoff itself; in most cases, the measure is linked to an asset and liability ratio able to capture and guarantee the solvability of the fund itself. Therefore, a full valuation of the obligation towards fund’s participants and the definition of an optimal investment strategy cannot exclude the proper appraisal of this additional option. The option payoff is conditional to a measurement asset that is different from the reference underlying asset. This structure recalls a barrier option with different measurement and payoff asset. The paper investigates the opportunity to apply barrier option scheme to the case of a pension fund, whose indexation target is conditional to a specific value of the funding ratio, in order to provide a full valuation of the obligation towards participants. The main objective is to provide a value for the inflation indexation as embedded option. Results derive from a simulation procedure applied to an exemplar case by means of scenario-based analysis. Numerical results gives the opportunity to state the absolute value of the “inflation option” and the relative value with respect to the fund’s liability.