Money Market Instruments

Overview

Money market instruments as defined in the FINCAD Function library are short-term interest rate securities (usually with maturities less than one year). They fall into two classes. One class consists of Interest bearing securities like Certificates of Deposits (CD) or some types of commercial paper (CP). The other class consists of discount securities like T-Bills or Banker Acceptances (BA’s).

FINCAD Functions

Interest Bearing Securities

For money market securities that pay interest, for example Notes, Commercial Paper (CP), Certificates of Deposit (CD) and others, there are several functions:

aaMMkt_IAM_p()

Calculates price, accrued interest and risk statistics given the yield.

aaMMkt_IAM_y()

Calculates yield, accrued interest and risk statistics given the price.

aaMMkt_IAM_df()

Calculates price, yield, accrued interest and risk statistics given a discount factor curve.

Discount Securities

For discount securities, securities that are sold at a discount to par and pay no interest, Treasury Bills, Banker’s Acceptance (BA) and others, there are several functions:

aaMMkt_DS_p()

Calculates price, accrued interest and risk statistics given the yield.

aaMMkt_DS_y()

Calculates yield, accrued interest and risk statistics given the price.

aaMMkt_DS_df()

Calculates price, yield, accrued interest and risk statistics given a discount factor curve.

Description of Inputs

Input Argument	Description
d_v	Settlement / valuation date. This is the date at which the security will be priced.
d_m	Maturity date.
d_dated	Date from which interest starts to accrue. Is only for interest at maturity securities (aaMMkt_IAM*)
cpn	Coupon rate. Is only for interest at maturity securities (aaMMkt_IAM*)
princ_m	Principal at maturity
yield	The quoted yield. The type of yield is specified by the yield basis (yield_type) and the accrual (acc). Input to the _p functions (price from yield).
Yield_type	The basis of the yield. For interest at maturity securities, the yield basis is generally simple interest basis (= 7).
acc	Yield Accrual. In the money markets, the yield accrual is generally act/365 (= 1) or act/360 (= 2).
price	The clean price of the security (excluding accrued interest) per 100 of notional. Is only an input to the _y functions (yield from price).
Df_crv	A discount factor curve (date, discount factor). Is an input to the _df functions (price, yield from curve).
intrp	Interpolation method. How discount factors are interpolated from the discount factor curve.

Description of Outputs

Output Statistics	Description
Fair value	The fair value of the security (excluding accrued interest)
Accrued interest	The accrued interest (only for interest bearing paper, aaMMkt_IAM*)
Fair value + accrued	This is the dirty price of the bond = clean price + accrued interest
Duration	The Macaulay duration of the security. Depends on the yield basis, accrual.
Modified duration	The modified duration of the security. Depends on the yield basis, accrual.
Convexity	The convexity of the security. Depends on the yield basis, accrual.
Basis point value	The price change of the security for a one basis point change in the yield. The frequency and accrual of the yield is the same as those of the security.
Yield value of a bp change in price	The change in the yield assuming the security price (100 par) changes by 0.01.
Cashflow at maturity	The total cashflow at maturity. Is only returned for aaMMkt_IAM*.
Number of days of accrued interest	The number of days of accrued interest (only for interest bearing paper, mmMMkt_IAM*).

Example

Calculation of the Statistics

Consider a one-year interest bearing security that matures on 1-Aug-1998, and suppose that today’s date is 1-Jan-1998.

aaMMkt_IAM_p

Input Argument	Description	Example Data	Switch
d_v	value date	1-Jan-1998
d_m	maturity date	1-Aug-1998
d_dated	dated date	1-Aug-1997
npa	principal at maturity	100
cpn	coupon	5%
yield	yield to maturity	10%
yield_type	rate basis of yield rate	7	simple interest rate basis
acc	accrual method	2	actual/360
stat	list of statistics	1…10

Results

Output Statistics	Description	Value
1	clean price	97.10112802
2	accrued interest	2.125
3	dirty price	99.22612802
4	duration	0.588888889
5	modified duration	0.55613851
6	modified convexity	0.618580085
7	basis point value	-0.00551804
8	yield value of a basis point in price	-0.00018121
9	cashflow maturity date	105.0694444
10	number of days of accrued interest	153

We note that the accrual of time depends on the choice of the accrual method which in the case above is actual / 360 = # days / 360. There are many accrual methods, and we direct the user to the Day Count Conventions and Accrual Factors FINCAD Math Reference document for more details. Below, we will assume the act/360 setting of the example.

Accrued interest is calculated from the dated date (d_dated) to the value date and:

In the case above, it is not difficult to see that this is equal to 153 / 360 * 0.05 * 100.

Let be the Coupon (in the case of a discount security this is zero).

In our case = 5.069444 = 365/360 * 0.05 * 100

Let be the dirty price.

Let y be the yield, which in our example is quoted on a simple interest basis (yield_type = 7), with act/360 accrual. as a function of , is given by

where:

is the time (in years) from the value date to the maturity date calculated using the accrual method acc.

In our case = 212 / 360.

The derivative of with respect to is:

while the second derivative is:

Modified duration

Duration (macaulay)

Convexity

Basis point value is obtained by setting in the 2^nd order Taylor series expansion:

Note: This demonstrates how the modified duration and convexity can be used to approximate price changes as a function of changes in yield.

Yield value of a one basis point change in price is the derivative of the yield with respect to the price multiplied by 0.01.

Note 1 If the yield basis is not simple, for example discount rate basis (yield_type = 8), the discounting term, , is replaced by and the derivatives should be altered to reflect this. Everything else is the same. For annually compounded yields etc, this discounting term is replaced by and the derivatives are altered to reflect this change. For details on the compounded case, see the General Bond Functions FINCAD Math Reference document as a money market security is just a one period bond.

Note 2 For discount securities, simply set the accrued and the coupon equal to zero in the above equations.

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