Abstract

In this paper, we study the valuation of stochastic cash flows that exhibit dependence on interest rates. We focus on insurance liability cash flows linked to an index, such as a consumer price index or wage index, where changes in the index value can be partially understood in terms of changes in the term structure of interest rates. Insurance liability cash flows that are not explicitly linked to an index may still be valued in our framework by interpreting index returns as so-called claims inflation, i.e., an increase in claims cost per sold insurance contract. We focus primarily on the case when a deep and liquid market for index-linked contracts is absent or when the market price data are unreliable. Firstly, we present an approach for assigning a monetary value to a stochastic cash flow that does not require full knowledge of the joint dynamics of the cash flow and the term structure of interest rates. Secondly, we investigate in detail model selection, estimation and validation in a Heath–Jarrow–Morton framework. Finally, we analyze the effects of model uncertainty on the valuation of the cash flows and how forecasts of cash flows and interest rates translate into model parameters and affect the valuation.

Highlights

  • In this paper, we study the valuation of index-linked cash flows under the assumption that index returns and the changes in nominal interest rates have significant dependence

  • Q0 [I] = E [φkT IkT ] factors into a product, where one factor is the expected value of the part of the index value that cannot be explained by interest rates, and the other factor, completely specifying a generally accepted HJM forward-rate model, is the monetary value of the part of the index value that is explained by the interest rates

  • We present an approach, for assigning a monetary value to an index-linked cash flow, that does not require full knowledge of the joint dynamics of the cash flow and the term structure of interest rates

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Summary

Introduction

We study the valuation of index-linked cash flows under the assumption that index returns and the changes in nominal interest rates have significant dependence. The approach we promote for the valuation of index-linked cash flows requires accurate modeling of the dynamics of the yield curve of nominal interest rates. We apply the valuation principles in [3], in an HJM framework and based on historical yield-curve and index data, with the aim of setting up a credible valuation machinery for index-linked cash flows. Many insurance liability cash flows depend on yearly updated values of a consumer price index, whereas historical data of yearly yield curve changes are not sufficient for efficiently parameterizing an HJM model.

Preliminaries
Valuation of an Index-Linked Cash Flow
Model Selection and Validation
The Volatility Structure of Changes in the Forward Rates
The Market Price of Risk and Model Validation
The Relation between the Consumer Price Index and the Short Rate
Model-Based Valuation
Findings
Conclusions and Discussion
Full Text
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