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Pricing of the Cross-Currency Interest Rate Guarantee Embedded in Financial Contracts in a LIBOR Market Model

By Tsung-Yu Hsieh, Chi-Hsun Chou and Son-Nan Chen

Abstract

We derive the pricing formulae for the financial contracts, such as guaranteed investment contracts (GICs), life insurance contracts, pension plans, and others, with the guaranteed minimum rate of return set relative to a LIBOR interest rate. Further, we analyze the guaranteed contracts in which the asset that provides the underlying return for the contract and the guaranteed interest rate are denominated in different currencies, which is a common practice. The guaranteed contracts with the above characteristics are called “cross-currency interest rate guaranteed contracts” (CIRGCs). Valuation of such contracts has not been investigated in the previous literature. To value CIRGCs, a cross-currency LIBOR market model is introduced. The LIBOR market model for a single-currency economy is extended to a cross-currency economy which incorporates the traded-asset prices and exchange rate processes into the model setting. The cross-currency LIBOR market model (CLMM) is suitable and applicable to pricing a variety of CIRGCs. The pricing formulas derived under the CLMM are more tractable and feasible for practice than those derived under the instantaneous short rate model or the HJM model. Four different types of CIRGCs are priced in this article. Calibration procedures are also discussed for practical implementation. In addition, Monte-Carlo simulation is provided to evaluate the accuracy of the theoretical prices

Topics: Interest rate, guarantee, Cross-currency, LIBOR market model, Finance, HG1-9999, Social Sciences, H
Publisher: Kaizen Publications
Year: 2015
DOI identifier: 10.0612/article-2
OAI identifier: oai:doaj.org/article:1e5bc69f551d4a6e9350fb70aeaa85c7
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