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). 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.
關聯:
International Research Journal of Applied Finance 6(12), pp.761-795
