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Oracle Financial Services Reference Guide
Release 12.1
Part Number E13528-03
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Rate Conversion

This chapter describes how Oracle Transfer Pricing translates interest rates from their initial formats into formats that can be used by the application.

This chapter covers the following topics:

Overview of Rate Conversion

Interest rates are available in a variety of formats. In Oracle Transfer Pricing, interest rates are used for multiple purposes, each requiring a specific rate format. The application must apply transformation formulas to translate the interest rates from their initial formats into formats that can be used by Oracle Transfer Pricing.

Related Topics

Interest Rate Codes, Oracle Transfer Pricing User Guide

Characteristics of Interest Rates Codes

The following characteristics define an interest rate code:

The accrual basis can be:

The compound basis can be:

The rate format can be:

Discount factor is used only internally and cannot be specified as an input rate format in Oracle Transfer Pricing. It is well known that for bonds issued at par with payment frequency equal to the compound basis, the yield-to-maturity at origination or par yield is equal to the coupon.

There are several definitions of yield-to-maturity. Oracle Transfer Pricing does not use the unconventional true yield definition of Stigum but prefers instead the Wall Street convention.

Related Topics

Overview of Rate Conversion

Rate Format Usage

A few typical instances of rate format usage in Oracle Transfer Pricing are as follows:

Related Topics

Overview of Rate Conversion

Monte Carlo Rate Path Generation

The Monte Carlo Rate Path Generation process requires annually compounded Actual/Actual zero-coupon yield as the input. If the input IRC format is anything other than zero-coupon annual yield, a conversion process is applied.

Stochastic rates output from Monte Carlo are also annually compounded Actual/Actual zero-coupon yields.

Related Topics

Rate Format Usage

Rate Index Calculation from Monte Carlo Rate Paths

The Rate Index rule formulas are applied to the yields forecasted from the valuation curve in the Monte Carlo process. A formula for each additional IRC must exist in the Rate Index rule. The formulas are applied during processing when one of the additional IRCs is required for repricing individual instrument records.

Related Topics

Rate Format Usage

Use in Transfer Pricing Methods

A description of rate format usage in cash-flow based and noncash flow transfer pricing methods is given below.

Noncash Flow Methods

The noncash flow based transfer pricing methods use historical IRC data pulled directly from the historical rates tables. For these methods, the format of the IRC used as the transfer pricing yield curve is assumed to be a yield-to-maturity.

Cash Flow Methods

There are three cash flow methods:

Related Topics

Rate Format Usage

Rate Conversion Algorithms

Accrual basis or compounding basis conversions are quite straightforward. However, rate format conversions from zero-coupon yield to yield-to-maturity and vice versa, are difficult.

The following table describes terminology used in rate conversion algorithms used by Oracle Transfer Pricing.

Terminology used in Rate Conversion Algorithms
Symbol Name Notes
AI(Ti) Accrued interest for the i-th security  
C(Ti) Coupon value of the i-th security This is the true dollar value of the cash flow (not annualized)
m Compounding frequency (per year) Possible values are:
  • 12 (monthly)

  • 2 (semi-annual)

  • 1 (annual)

  • 0 (simple)

ni Number of full compounding periods from Calendar Period End Date up to term Ti  
P(T) Discount factor with term Ti Value of a zero-coupon bond Ti and par = $1
r Total number of securities  
Ti Term in Act/Act years of the i-th security Sorted in ascending order
L(i,k) Time in Act/Act years of the start of the k-th (k=0... ni) compounding period for security i  
wi Residual number of compounding periods between the current date and the next compounding date for i-th security  
yTM(Ti) Yield-to-maturity of the i-th security  
yzc(Ti) Zero-coupon yield of the i-th security  

The yield curve is composed of r par bonds with different terms. Par value is equal to $1.

The zero-coupon yield is the vector of r values yzc(Ti) that solves the following equations:

Equation A

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Equation B

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The yield-to maturity for the i-th security is the value yTM(Ti) that solves the following equations:

Equation C

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Equation D

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Related Topics

Overview of Rate Conversion

Conversion From Yield-to-Maturity to Zero-Coupon Yield

The system first calculates the values c(Ti) and AI(Ti) based on the following equations:

Then the system bootstraps the yield curve using the BFGS algorithm to solve the following equations:

Related Topics

Rate Conversion Algorithms

Conversion From Zero-Coupon Yield to Yield-to-Maturity

The system first calculates the values c(Ti) and AI(Ti) based on the following equations:

Then, the system solves these equations following the Newton-Raphson algorithm.

Related Topics

Rate Conversion Algorithms