13.17.1 General Case

The user can enter the following formula for each index and index term:

Figure 13-15 Index Case and Term Formula

Description of formula to calculate the each index and index term follows:

Where:

ai are coefficients, ai Š 0

bi are exponents; they can be integer only

ω refers to the Monte Carlo scenario

Tk is the term of the index for which the formula applies

τi is the term of each forecasted risk-free rate

R(t,t+τi,ω) is the risk-free rate at time t for a term of τi

In this formula, we included the scenario ω for notational convenience, although it cannot be specified by the user: the same formula is applied for each scenario - what varies is the risk-free rate. The user can specify only ai, bi, Tk,τi, and of course of the identity of the Index IRC for which the formula applies.

If an adjustable instrument in the database is linked to an index term for which the user did not define a formula, the engine will linearly interpolate (or extrapolate) along with the term.

Suppose the user-defined formulae only for Libor 1 month and Libor 5 months, but an instrument record is linked to Libor 3 months, the engine will calculate the index rate for Libor 3 months as the average of Libor 1 month and 5 months.