Abstract

In this paper we focus on the concept of a discount rate. In [1] one expressed some concerns regarding the models that present randomization of the discount rate. This paper proposed a new approach to the construction of variable deterministic and stochastic interest rates. This approach is based on the concept of forward rate. In [1, 2] we introduced a new analytical model of popular rate LIBOR. This rate is commonly used in the construction of price instruments that include the euro-dollar exchange rate components. LIBOR is by definition is the average deposit rates of the world's major banks. Valuations of the LIBOR is based on survey Alternative construction of the euro-dollar rate contract may use a synthetic approach. This approach follows the model of LIBOR proposed in [1]. The synthetic approach involves the price value, which consists of the price of its constituent components. This interpretation implies that the LIBOR rate to be charged for deposit of one dollar in the risk free Bank at the initial time which then immediately converts it to the British pounds. The resulting amount is invested then in risk-free British bonds for the period of the contract. At the end of this period, cumulated amount is converted back into dollars. Calculated interest rate represents an analytical representation of a dollar deposit to the risk free Bank while LIBOR rate is the average of the top panel of banks. In [2] we synthetically constructed price associated with LIBOR. Hence, the standard modeling of the LIBOR deals with empirical data rather than with its formal definition.

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