10.1.2 Definitions

Neither the static spread nor the OAS can be defined directly as they are solutions of two different equations. We give hereafter a simplified version of the equations that the system solves, using the assumptions described earlier. The static spread is the value ss that solves the following equation:

Equation 1

Figure 10-1 Equation 1

Description of the Transfer Pricing Option Cost Equation 1 follows:

Where:

Table 10-1 Transfer Pricing Option Cost Equation 1

:MV	market, or book, or par value of the instrument (as selected in the Transfer Pricing rule)
CF(k)	cash flow occurring at the end of month k along with the forward rate scenario
:f(j)	forward rate for month j
∆t	length (in years) of the compounding period; hard-coded to a month, such as 1/12

In the Monte Carlo Methodology, the option adjusted-spread is the value OAS that solves the following equation:

Equation 2:

Figure 10-2 Equation 2

Description of the Transfer Pricing Option Cost Equation 2 follows:

Where:

Table 10-2 Transfer Pricing Option Cost Equation

: N	total number of Monte Carlo scenarios
CF(K,ω)	cash flow occurring at the end of month k along scenario ω
D(k, ω,OAS)	fstochastic discount factor at the end of month k along scenario ω for a particular OAS

• Cash Flows are calculated up till maturity even if the instrument is adjustable.

  Note:

  Otherwise, the calculations would not catch the cost of caps or floors.
• In the real calculations, the formula for the stochastic discount factor is simplified.