Perturbational bills

Introduction

The perturbational bank bill (or perturbational bill) type allows a bank bill's price/yield dependency to be modelled using only the security's risk numbers. It is in all other ways identical to a bank bill.

Security description

The perturbational approach does not require any information about the cash-flow structure of the security. Instead, the user supplies a set of risk numbers that describe how the security’s return is affected by the passage of time and by changes in the yield curve. The return over a given interval is calculated using the following expression:

<math>r = -MD \cdot \delta y\,</math>

where

<math>r\,</math> is the return of the security over the interval;

<math>MD\,</math> is the modified duration of the security, expressed in years;

<math>\delta y\,</math> is the change in the security’s zero coupon yield at the maturity date.

Note that this differs from the return for a coupon-paying security in that there is no time-driven term. Zero-coupon securities do not generate accrued interest, so their only source of return is the yield curve.

The cash flow structure of a zero-coupon security is typically a single cash flow at maturity. This is consistent with the underlying assumptions of the perturbational approach, so the algorithm will give results that are equal in accuracy to a conventional pricing approach.

Security code

A perturbational zero-coupon security has pricing type PERTURBATIONAL_BILL.

Calculation of returns

No pricing is carried out for this type of security. Instead, returns are calculated directly using the expression in the section above.

Security file setup

A bank bill is set up as follows:

The security formats for a conventional bill and a perturbational bill are identical, apart from the security type.

Returns file setup

A perturbational bill requires the following information in the returns file:

In addition, information on the bill's convexity can also be supplied, if available:

Unlike a conventional bill, a perturbational bill must have values supplied for fields 7 (yield to maturity) and 8 (modified duration).

Example 1

A bank bill is issued in AUD with a maturity date of 15th June 2011. The bill has a AAA credit rating, and is priced off the AUD_CURVE yield curve.

This security is represented by a single entry in the security definition file:

The Start date field is left blank, indicating that all supplied characteristics remain unchanged during the bill's lifetime.

The security has the corresponding entries in the returns file:

These records show the weight and returns of the bill over successive days within the STF1 portfolio. Values for convexity have been supplied, although these are optional.

Example 2

A bill is issued in USD with maturity date 20th Dec 2011. At issue, the bill was assigned a AA credit rating but was downgraded to AA- on 15th June 2011. This security is represented by two entries in the security definition file:

Both rows are identical except for the entries in the Start date and Credit rating column.

Introduction

The perturbational bank bill (or perturbational bill) type allows a bank bill's price/yield dependency to be modelled using only the security's risk numbers. It is in all other ways identical to a bank bill.

Security description

The perturbational approach does not require any information about the cash-flow structure of the security. Instead, the user supplies a set of risk numbers that describe how the security’s return is affected by the passage of time and by changes in the yield curve. The return over a given interval is calculated using the following expression:

<math>r = -MD \cdot \delta y\,</math>

where

<math>r\,</math> is the return of the security over the interval;

<math>MD\,</math> is the modified duration of the security, expressed in years;

<math>\delta y\,</math> is the change in the security’s zero coupon yield at the maturity date.

Note that this differs from the return for a coupon-paying security in that there is no time-driven term. Zero-coupon securities do not generate accrued interest, so their only source of return is the yield curve.

The cash flow structure of a zero-coupon security is typically a single cash flow at maturity. This is consistent with the underlying assumptions of the perturbational approach, so the algorithm will give results that are equal in accuracy to a conventional pricing approach.

Security code

A perturbational zero-coupon security has pricing type PERTURBATIONAL_BILL.

Calculation of returns

No pricing is carried out for this type of security. Instead, returns are calculated directly using the expression in the section above.

Security file setup

A bank bill is set up as follows:

The security formats for a conventional bill and a perturbational bill are identical, apart from the security type.

Returns file setup

A perturbational bill requires the following information in the returns file:

In addition, information on the bill's convexity can also be supplied, if available:

Unlike a conventional bill, a perturbational bill must have values supplied for fields 7 (yield to maturity) and 8 (modified duration).

Example 1

A bank bill is issued in AUD with a maturity date of 15th June 2011. The bill has a AAA credit rating, and is priced off the AUD_CURVE yield curve.

This security is represented by a single entry in the security definition file:

The Start date field is left blank, indicating that all supplied characteristics remain unchanged during the bill's lifetime.

The security has the corresponding entries in the returns file:

These records show the weight and returns of the bill over successive days within the STF1 portfolio. Values for convexity have been supplied, although these are optional.

Example 2

A bill is issued in USD with maturity date 20th Dec 2011. At issue, the bill was assigned a AA credit rating but was downgraded to AA- on 15th June 2011. This security is represented by two entries in the security definition file:

Both rows are identical except for the entries in the Start date and Credit rating column.