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Nelson-Siegel model of the term structure of interest

You work in the risk management department of the defined-benefit pension fund DBPF. It is your responsibility to report on the funding position of DBPF to your line manager every working day by 11 o’clock. Your daily routine is as follows: every morning at 9 o’clock, you receive values from DBPF’s research department for the parameters of the Nelson-Siegel model of the term structure of interest rates:

𝑟(𝜏)=𝑎+𝑏∙[1−exp{−𝜏𝜃}𝜏𝜃]+𝑐∙exp⁡{−𝜏/𝜃}

You use then this term structure model to value DBPF’s assets. The assets are exclusively bonds. You also use the model to value DBPF’s obligations towards its policyholders. Once you have the value of assets and the value of obligations, you compute DBPF’s current funding position. Furthermore, you assess the sensitivity of this position to changes in interest rates using the modified duration.

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