Floating Rate Notes with Averaging (muni / tax-exempt market)

Overview

The suites of functions described in this document calculate cash flows, price, and yield for FRNs (or Variable Rate Bonds) whose payments are based upon the arithmetic average of the reset rates. This is in contrast to functions such as aaFRN and aaFRN_cfm_FRN, which use compounded reset rates. For example, if a payment period is comprised of exactly two reset periods, with reset rates r’ and r’’, then the payment on an average rate coupon is based upon (r’+r’’)/2, whereas the payment on a compounded coupon is based upon (1+r’)(1+r’’)-1. The average rate is actually calculated as a weighted average, using the notional times the length of each reset period as the weight.

There are three sets of functions available for average rate FRNs. The first set of functions, aaFRNavg and aaFRNavg_cf, generate the coupon dates and the reset period dates, and use an accruing curve and a discounting curve to calculate cash flows, price, and yield to maturity. There is also a function, aaFRNavg_Tables, which can be used to calculate the active reset dates, which are needed as an input table to the above functions.

In the second set of functions, aaFRNavg_fs and aaFRNavg_fs_cf, the coupon dates, reset dates, notional dates, and fixed payment dates are completely user defined (freestyle), allowing for totally arbitrary periods to be defined. The notional table and fixed payment table allow for an amortizing notional. The functions take in an accruing curve for calculating future reset rates, and a discounting curve for discounting cash flows, and calculate cash flows, price, and yield to maturity. The function aaFNRavg_Tables_fs can be used to calculate the coupon dates, reset dates, and amortization dates needed for the input tables to the above functions.

In the third set of functions, aaFRNavg_FixFwds_fs_cf, aaFRNavg_FixFwds_fs_p, and aaFRNavg_FixFwds_y, the coupon dates, reset dates, notional dates, and fixed payment dates are also completely user defined (freestyle), allowing for totally arbitrary periods. These functions, however, do not take in an accruing curve or a discounting curve. Active and future reset rates can be given in the input reset table, where rates that are not given are assumed to be equal to the previous rate given in the reset table. The behavior of the reset table is described in more detail in the Formulas & Technical Details section below. For pricing the FRN or floating leg of a swap, cash flows are priced using the given yield, rate basis, and accrual method. The function aaFRNavg_Tables_fs can be used to calculate the dates for the input tables for these functions.

Formulas & Technical Details

Reset rate calculation

For the functions aaFRNavg, aaFRNavg_cf, aaFRNavg_fs, and aaFRNavg_fs_cf, active reset rates are entered in the reset table, and future reset rates are calculated using forward rates from a given accruing curve.

For the reset period, let:

be the forward rate

be the accrual factor from the effective date to the terminating date of the reset period calculated using acc_reset

be the discount factor from the accruing curve at the terminating date of the reset period

be the discount factor from the accruing curve at the effective date of the reset period

Then:

Equation 1

For the functions aaFRNavg_FixFwds_fs_p, aaFRNavg_FixFwds_fs_y, and aaFRNavg_FixFwds_fs_y, no accruing curve is used, and active and future reset rates can be given in the input reset table. For periods where the rate is not given or is equal to 0, the previous non-zero rate given will be used. This is described in more detail below.

Average rate calculation

For a particular coupon period, for the reset period, let:

be the accrual factor from the effective date to the terminating date of the reset period calculated using acc_pay

be the notional principal amount

be the spread over the reset

The difference between the subscript and subscript is that subscript counts split reset periods (in cases where a coupon date or an amortization date occurs within a reset period), whereas subscript refers to complete reset periods.

Then:

’

Equation 2

and:

Equation 3

Hence the average rate is the weighted average of the reset rates (or forward rates), using the quantity as the weight. This quantity is shown in column 8 of the Reset Table (table_type = 2) that is output by aaFRNavg_cf, aaFRNavg_fs_cf, and aaFRNavg_FixFwds_fs_cf.

If the margin () is constant for all periods (as it is in aaFRNavg and aaFRNavg_cf), then the formula for the average rate reduces to:

Equation 4

aaFRNavg_FixFwds_fs_* reset rates

This set of functions does not take in an accruing curve for calculating future reset rates. Instead, the future rates can be given in the input reset table. Reset rates are taken from the reset table using the following rules:

1. For a given reset period, if the rate is given in the reset table (for active or future resets), then the given rate and margin are used for that period

2. For a given reset period, if the reset rate is not given or is equal to 0, then the previous non-zero rate given will be used for this period

3. For a given reset period, if a non-zero margin is given, this margin will be used regardless of whether or not the rate was given for this period

4. For a given reset period, if the margin is not given or is equal to 0, then the previously used margin will be used for this period

5. If the terminating date of the last reset period given is prior to the last coupon payment date, then the function will insert a reset period effective from the last reset period terminating date given to the last coupon payment date. The reset rate for this period will be the previous non-zero rate given

The actual reset rates that are used by the functions can be verified by examining the Reset Table (table_type = 2) that is output by the function aaFRNavg_FixFwds_fs_cf.

aaFRNavg_FixFwds_fs_* risk statistic calculations

The price and yield functions output several risk statistics: Duration, Modified Duration, Convexity, Basis Point Value, and Effective Duration. Some of these statistics are calculated using a finite difference method. The reset rates for periods that reset after the value date will be bumped by a small amount. The yield, rate basis, and accrual method being used to price the cash flows can be used to calculate a forward rate for each coupon period. These forward rates are bumped by the same small amount as the reset rates. These bumped forward rates are then used to discount cash flows that are calculated using the bumped future reset rates. A central difference approximation is used to calculate Effective Duration and Convexity, as follows:

Equation 5

Equation 6

where

is the size of the bump,

is the dirty price,

is the dirty price using bumped up rates, and

is the dirty price using bumped down rates.

These statistics are used to calculate Basis Point Value (BPV):

Equation 7

where .

Duration and Modified duration are calculated from the cash flows (which are generated using the function FRNavg_FixFwds_cf) similar to the way duration and modified duration are calculated for bonds (see the General Bond Functions FINCAD Math Reference document).

FINCAD Functions

aaFRNavg(d_v, d_dated, d_m, d_f_cpn, d_l_cpn, freq, d_rul_pay, d_reset_cycle, reset_freq, d_rul_reset, reset_mktdays, reset_tbl, mgn, npa, redemp_val, hl, df_crv_acc, df_crv_disc, acc_rt, acc_pay, intrp, position, stat)

Calculates the fair value, accrued interest and various yields for an average-rate FRN or floating leg with regular coupons and resets. The coupons may be annual, semi-annual, quarterly, monthly, biweekly, weekly and 35 days. The resets can be on a separate cycle at any of those frequencies plus daily. The function allows the input of separate accruing and discounting curves.

aaFRNavg_cf(d_v, d_dated, d_m, d_f_cpn, d_l_cpn, freq, d_rul_pay, d_reset_cycle, reset_freq, d_rul_reset, reset_mktdays, reset_tbl, mgn, npa, redemp_val, hl, df_crv_acc, df_crv_disc, acc_rt, acc_pay, intrp, position, table_type)

Calculates the future cash flows, present value of future cash flows and reset rates for average-rate FRNs with regular coupons and resets.

aaFRNavg_Tables(d_v, d_dated, d_m, d_f_cpn, d_l_cpn, freq, d_rul_pay, d_reset_cycle, reset_freq, d_rul_reset, reset_mktdays, hl, table_type)

Calculates various dates related to average-rate FRNs with regular coupons and resets. For instance, it calculates the dates for all active resets. This is a utility function which helps set up the input tables for calls to aaFRNavg and aaFRNavg_cf.

aaFRNavg_fs(d_v, payperiod, npa_tbl, reset_tbl, flleg_fixpay, df_crv_acc, df_crv_disc, acc_rt, acc_pay, intrp, position, stat)

Calculates the fair value, accrued interest and various yields for an average-rate FRN or floating leg with user specified coupon dates, reset dates, notional schedule, and notional payments. The function allows the input of separate accruing and discounting curves.

aaFRNavg_fs_cf(d_v, payperiod, npa_tbl, reset_tbl, flleg_fixpay, df_crv_acc, df_crv_disc, acc_rt, acc_pay, intrp, position, stat)

Calculates the future cash flows, present value of future cash flows and reset rates for an average-rate FRN or floating leg with user specified coupon dates, reset dates, notional schedule, and notional payments.

aaFRNavg_Tables_fs(d_v, d_dated, d_m, d_f_cpn, d_l_cpn, freq, d_rul_pay, d_reset_cycle, reset_freq, d_rul_reset, reset_mktdays, d_f_amort, d_l_amort, amort_freq, d_rul_amort, amort_type, hl, table_type)

Calculates various dates related to average-rate FRNs with user specified coupon dates, reset dates, notional schedule and notional payments. This is a utility function which helps set up the input tables for calls to aaFRNavg_fs, aaFRNavg_fs_cf, and aaFRNavg_FixFwds_fs_*.

Note: Examples of how to use the above functions are contained in the FINCAD pre-built workbooks.

aaFRNavg_FixFwds_fs_cf(d_v, payperiod, npa_tbl, reset_tbl, flleg_fixpay, acc_pay, position, table_type)

Calculates the future cash flows and reset rates for an average-rate FRN or floating leg with user specified coupon dates, reset dates, notional schedule, and notional payments. Active and future reset rates are taken from the input reset table. If a rate is missing or 0 for a given period, the previous known rate in the table will be used.

aaFRNavg_FixFwds_fs_p(d_v, payperiod, npa_tbl, reset_tbl, flleg_fixpay, yield, yield_basis, acc_pay, position, stat)

Calculates price given a yield and rate basis for an average-rate FRN or floating leg with user specified coupon dates, reset dates, notional schedule, and notional payments. Active and future reset rates are taken from the input reset table. If a rate is missing or 0 for a given period, the previous known rate in the table will be used.

aaFRNavg_FixFwds_fs_y(d_v, payperiod, npa_tbl, reset_tbl, flleg_fixpay, price, acc_pay, position, stat)

Calculates yield given price for an average-rate FRN or floating leg with user specified coupon dates, reset dates, notional schedule, and notional payments. Active and future reset rates are taken from the input reset table. If a rate is missing or 0 for a given period, the previous known rate in the table will be used.

Description of Inputs

aaFRNavg, aaFRNavg_cf, aaFRNavg_Tables

Input Argument	Description
d_v	value (settlement) date
d_dated	dated date - date from which accrued interest is calculated on newly issued securities
d_m	maturity date
d_f_cpn	date of first coupon after dated date
d_l_cpn	date of last coupon prior to maturity date
freq	cash flow frequency
d_rul_pay	business day convention for payment dates
d_reset_cycle	any reset period effective date. Is used to establish the reset period cycle.
reset_freq	reset period frequency
d_rul_reset	business day convention for reset dates *
reset_mktdays	number of business days prior to the reset date that the rate is fixed
reset_tbl	table containing active reset information. Dates may be calculated using aaFRNavg_Tables.
mgn	margin above or below a floating rate
npa	notional principal amount
redemp_val	redemption value at maturity (per 100 notional)
hl	holiday list
df_crv_acc	discount factor curve for accruing rates
df_crv_disc	discount factor curve for discounting rates
acc_rt	accrual method for reset rates
acc_pay	accrual method for coupon payments
intrp	interpolation method
position	trade position - long or short
table_type	output table type selection
stat	output statistic(s) selection

aaFRNavg_fs, aaFRNavg_fs_cf

Input Argument	Description
d_v	value (settlement) date
payperiod	table defining the coupon payment dates
npa_tbl	table specifying the amortization schedule for the notional principal amount
reset_tbl	table defining the reset periods
flleg_fixpay	table of fixed payment dates (e.g. exchange of principal)
df_crv_acc	discount factor curve for accruing rates
df_crv_disc	discount factor curve for discounting rates
acc_rt	accrual method for reset rates
acc_pay	accrual method for coupon payments
intrp	interpolation method
position	trade position - long or short
table_type	output table type selection
stat	output statistic(s) selection

aaFRNavg_fs_Tables

Input Argument	Description
d_v	value (settlement) date
d_dated	dated date - date from which accrued interest is calculated on newly issued securities
d_m	maturity date
d_f_cpn	date of first coupon after dated date
d_l_cpn	date of last coupon prior to maturity date
freq	cash flow frequency
d_rul_pay	business day convention for payment dates
d_reset_cycle	any reset period effective date that is used to establish the reset period cycle.
reset_freq	reset period frequency
d_rul_reset	business day convention for reset dates *
reset_mktdays	number of business days prior to the reset date that the rate is fixed
d_f_amort	first amortization after dated date (optional)
d_l_amort	last amortization before maturity (optional)
amort_freq	amortization frequency
d_rul_amort	business day convention for amortizations
amort_type	defines whether or not the amortization is independent of coupon dates
hl	holiday list
table_type	table type

aaFRNavg_FixFwds_fs_cf, aaFRNavg_FixFwds_fs_p, aaFRNavg_FixFwds_fs_y

Input Argument	Description
d_v	value (settlement) date
payperiod	table defining the coupon payment dates
npa_tbl	table specifying the amortization schedule for the notional principal amount
reset_tbl	table defining the reset periods
flleg_fixpay	table of fixed payment dates (e.g. exchange of principal)
yield	yield to maturity
yield_basis	rate basis of yield to maturity
price	clean price
acc_pay	accrual method for coupon payments
position	trade position - long or short
table_type	output table type selection
stat	output statistic(s) selection

(*) The “Third Wednesday” setting is included in this switch for standardization with other functions; however this setting is not recommended and does not have a practical application for this instrument class.

Description of Outputs

Pricing functions

aaFRNavg and aaFRNavg_fs

Statistics	Description
pricing statistics:	fair value, accrued interest, and fair value + accrued interest
yield to maturity statistics:	annually compounded, semi-annually compounded, …

aaFRNavg_FixFwds_fs_p

Statistics	Description
pricing statistics:	fair value, accrued interest, and fair value + accrued interest
risk statistics:	duration, modified duration, effective duration, convexity, basis point value

Yield functions

aaFRNavg_FixFwds_fs_y

Statistics	Description
yield statistics:	annually compounded, semi-annually compounded, …
risk statistics:	duration, modified duration, effective duration, convexity, basis point value

Cash flow functions

aaFRNavg_cf, aaFRNavg_fs_cf, and aaFRNavg_FixFwds_fs_cf

These functions output three different tables:

Output Table	Description
Cash flows:	contains all future cash flow information (interest payments, principal payments, accrued interest).
Reset table:	contains all information related to the reset periods. The date of associated coupon is given in the first column. A reset period will be split if a coupon date or an amortization date occurs within it.
Interest summary table:	contains information related to the coupons, (e.g. average rate, interest payment, accrued interest)

aaFRNavg, aaFRNavg_fs

Output Statistics	Description
1	fair value
2	accrued interest
3	value of future cash flows (fair value + accrued)
4	annually compounded yield
5	semi-annually compounded yield
6	quarterly compounded yield
7	monthly compounded yield

aaFRNavg_cf, aaFRNavg_fs_cf

Table Type	Description
1	Cash Flows - 8 col: date, interest, principal, total cash flow, PV interest, PV principal, PV total cash flow, accrued interest
2	Reset Table - 10 col: payment date, rate fixing date, rate effective date, rate terminating date, notional, rate, rate + margin, weight, interest, accrued interest
3	Interest Summary Table - 4 col: payment date, average coupon, interest, accrued interest

aaFRNavg_Tables

Table Type	Description
1	Payment Dates Table (effective date, terminating date )
2	Reset Dates Table (rate fixing date, rate effective date, rate terminating date)
3	Active Reset Table (rate fixing date, rate effective date, rate terminating date)

aaFRNavg_Tables_fs

Table Type	Description
1	Payment Dates Table (effective date, terminating date )
2	Reset Dates Table (rate fixing date, rate effective date, rate terminating date)
3	Active Reset Table (rate fixing date, rate effective date, rate terminating date)
4	Notional Table (effective date, terminating date)

aaFRNavg_FixFwds_fs_p

Output Statistics	Description
1	fair value
2	accrued interest
3	fair value + accrued interest
4	duration
5	modified duration
6	convexity
7	basis point value
8	number of days of accrued interest
9	effective duration

aaFRNavg_FixFwds_fs_y

Output Statistics	Description
1	annually compounded yield
2	semi-annually compounded yield
3	quarterly compounded yield
4	monthly compounded yield
5	simple yield
6	accrued interest
7	fair value + accrued interest
8	duration
9	modified duration
10	convexity
11	basis point value
12	number of days of accrued interest
13	effective duration

aaFRNavg_FixFwds_fs_cf

Table Type	Description
1	Cash Flows - 5 col: date, interest, principal, total cash flow, accrued interest
2	Reset Table - 10 col: payment date, rate fixing date, rate effective date, rate terminating date, notional, rate, rate + margin, weight, interest, accrued interest
3	Interest Summary Table - 4 col: payment date, average coupon, interest, accrued interest

Examples

Example 1: aaFRNavg and aaFRNavg_cf

Suppose today is 14-Feb-2005, and we want to calculate the cash flows, price, and yield to maturity of an FRN using average rate coupons. The FRN was issued on 24-Feb-2004, and will mature on 24-Feb-2006. Coupons are paid monthly, and the rates are reset weekly on Wednesday, effective on Thursday. There is a 1% margin above the floating rate.

The first step is to construct a reset table containing the dates and reset rates for the active reset periods. The active reset dates can be calculated using the function aaFRNavg_Tables with the following inputs.

aaFRNavg_Tables

Argument	Description	Example Data	Switch
d_v	value (settlement) date	14-Feb-2005
d_dated	dated date
d_m	maturity date	24-Feb-2006
d_f_cpn	date of first coupon after dated date
d_l_cpn	date of last coupon prior to maturity date
freq	cash flow frequency	4	monthly
d_rul_pay	business day convention for payment dates	1	no adjustment
d_reset_cycle	reset cycle date	17-Feb-2005
reset_freq	reset frequency	6	weekly
d_rul_reset	business day convention for reset dates	1	no adjustment
reset_mktdays	number of business days prior to the reset date that the rate is fixed	1
hl	holiday list (not needed in this example since no date adjustments are made)	0
table_type	table type	3	active reset table

This gives us the following active reset table:

reset date	effective date	terminating date
19-Jan-2005	20-Jan-2005	27-Jan-2005
26-Jan-2005	27-Jan-2005	3-Feb-2005
2-Feb-2005	3-Feb-2005	10-Feb-2005
9-Feb-2005	10-Feb-2005	17-Feb-2005

We must then add a fourth column to this table, in which we specify the known active reset rates. This four column reset table will then be used as input into aaFRNavg and aaFRNavg_cf.

reset date	effective date	terminating date	reset rate
19-Jan-2005	20-Jan-2005	27-Jan-2005	5.00%
26-Jan-2005	27-Jan-2005	3-Feb-2005	5.05%
2-Feb-2005	3-Feb-2005	10-Feb-2005	5.10%
9-Feb-2005	10-Feb-2005	17-Feb-2005	5.15%

Next, we need a discount factor curve that will be used for accruing rates. This curve will be used to calculate the forward rates for all future reset periods. For this example, we will use the following curve:

date	discount factor
14-Feb-2005	1
15-May-2005	0.987342
15-Aug-2005	0.974088
15-Nov-2005	0.960392
15-Feb-2006	0.945762
15-May-2006	0.932451

We also need a discount factor curve that will be used to discount the cash flows to the value date. For simplicity, in this example we will assume that the accruing curve and the discounting curve are the same.

We can now call aaFRNavg_cf and aaFRNavg to calculate the cash flows, price and yield to maturity of the FRN:

aaFRNavg_cf and aaFRNavg

Argument	Description	Example Data	Switch
d_v	value (settlement) date	14-Feb-2005
d_dated	dated date
d_m	maturity date	24-Feb-2006
d_f_cpn	date of first coupon after dated date
d_l_cpn	date of last coupon prior to maturity date
freq	cash flow frequency	4	monthly
d_rul_pay	business day convention for payment dates	1	no adjustment
d_reset_cycle	reset cycle date	17-Feb-2005
reset_freq	reset frequency	6	weekly
d_rul_reset	business day convention for reset dates	1	no adjustment
reset_mktdays	number of business days prior to the reset date that the rate is fixed	1
reset_tbl	active reset table	see above
mgn	margin above or below a floating rate	1%
npa	notional principal amount	100,000
redemp_val	redemption value (per 100 notional)	100
hl	holiday list (not needed in this example since no date adjustments are made)	0
df_crv_acc	discount factor curve for accruing rates	see above
df_crv_disc	discount factor curve for discounting rates	see above
acc_rt	accrual method for reset rates	1	actual/365 (fixed)
acc_pay	accrual method for coupon payments	1	actual/365 (fixed)
intrp	interpolation method	3	exponential
position	trade position	1	long
table_type	table type (cash flow function)	1	cash flows
stat	output statistic(s) (price and yield function)	{1, 2, …, 7}

Results: aaFRNavg_cf

date	interest	principal payment	total cash flow	present value of interest	present value of principal payment	present value total of cash flows	accrued interest
24-Feb-2005	519.70	0	519.70	518.96	0	518.96	349.73
24-Mar-2005	477.70	0	477.70	475.11	0	475.11	0
24-Apr-2005	528.88	0	528.88	523.68	0	523.68	0
24-May-2005	515.58	0	515.58	508.31	0	508.31	0
24-Jun-2005	540.55	0	540.55	530.50	0	530.50	0
24-Jul-2005	523.11	0	523.11	511.13	0	511.13	0
24-Aug-2005	547.57	0	547.57	532.56	0	532.56	0
24-Sep-2005	562.32	0	562.32	544.31	0	544.31	0
24-Oct-2005	544.18	0	544.18	524.32	0	524.32	0
24-Nov-2005	575.27	0	575.27	551.56	0	551.56	0
24-Dec-2005	583.03	0	583.03	556.21	0	556.21	0
24-Jan-2006	602.46	0	602.46	571.79	0	571.79	0
24-Feb-2006	594.87	100,000.00	100,594.87	561.71	94,425.72	94,987.44	0

Results: aaFRnavg

Statistic	Description	Value
1	fair value	100,986.15
2	accrued interest	349.73
3	value of future cash flows (fair value + accrued)	101,335.88
4	annually compounded yield	5.735%
5	semi-annually compounded yield	5.655%
6	quarterly compounded yield	5.616%
7	monthly compounded yield	5.590%

Example 2: aaFRNavg_FixFwds_p and aaFRNavg_FixFwds_cf

Suppose today is 5-Feb-2005, and we want to evaluate an FRN based on average rate coupons, but do want to use an accruing curve or a discounting curve. The FRN was issued on 1-Jan-2005, and matures on 1-Jul-2007. The notional is fixed at $100,000, which will be paid on the maturity date of 1-Jul-2007. Coupons are paid quarterly, and rates reset semi-annually. The first reset date was 1-Jan-2005, at which time the rate reset at 5%. Suppose we want all future reset rates to be 5.5%. If we are using the aaFRNavg_FixFwds_* functions, future rates can be specified in the input reset table. Future rates that are not given are set equal to the previous known rate in the table. Thus, for the 1-Jul-2005 reset date, the rate of 5.5% can be specified in the table, and all future reset periods will also use 5.5%.

Since these are user defined (freestyle) functions, dates must be given in the input tables for the coupon periods, reset periods, notional amounts, and fixed payments. The notional is constant, and there is only one fixed payment, at maturity, so the notional table and fixed payment table will each contain only one date. The coupon payment table and reset table can be constructed using the function aaFRNavg_Tables_fs, given the following inputs:

aaFRNavg_Tables_fs

Argument	Description	Example Data	Switch
d_v	value (settlement) date	5-Feb-2005
d_dated	dated date
d_m	maturity date	1-Jul-2007
d_f_cpn	date of first coupon after dated date
d_l_cpn	date of last coupon prior to maturity date
freq	cash flow frequency	3	quarterly
d_rul_pay	business day convention for payment dates	1	no adjustment
d_reset_cycle	reset cycle date	1-Jan-2005
reset_freq	reset frequency	2	semi-annual
d_rul_reset	business day convention for reset dates	1	no adjustment
reset_mktdays	number of business days prior to the reset date that the rate is fixed	0
d_f_amort	first amortization after dated date (optional)
d_l_amort	last amortization before maturity (optional)
amort_freq	amortization frequency	1	annual
d_rul_amort	business day convention for amortizations	1	no adjustment
amort_type	amortization rule	1	independent of payments
hl	holiday list (not needed in this example since no date adjustments are made)	0
table_type	table type	1, 2	payment and reset tables

This function will output both the coupon payment dates table, and the reset dates table. The coupon dates table can be used as is by the aaFRNavg_FixFwds_fs_* functions, but the reset table needs two extra columns; one for the reset rate, and one for the margin above or below the reset rate. All four tables needed by aaFRNavg_FixFwds_fs_* for this example are given below:

Payment Periods Table (table_type = 1)

effective date	terminating date
1-Jan-2005	1-Apr-2005
1-Apr-2005	1-Jul-2005
1-Jul-2005	1-Oct-2005
1-Oct-2005	1-Jan-2006
1-Jan-2006	1-Apr-2006
1-Apr-2006	1-Jul-2006
1-Jul-2006	1-Oct-2006
1-Oct-2006	1-Jan-2007
1-Jan-2007	1-Apr-2007
1-Apr-2007	1-Jul-2007

Notional Table

date	notional principal amount
1-Feb-2005	100,000

Reset Table (table_type = 2 = all reset periods)

reset date	effective date	terminating date	reset rate	margin
1-Jan-2005	1-Jan-2005	1-Jul-2005	5.000%	0.000%
1-Jul-2005	1-Jul-2005	1-Jan-2006	5.500%	0.000%
1-Jan-2006	1-Jan-2006	1-Jul-2006
1-Jul-2006	1-Jul-2006	1-Jan-2007
1-Jan-2007	1-Jan-2007	1-Jul-2007

Note that these functions do not require all of the reset periods to be defined in the reset table. The last rate given, 5.5% in this case, is going to be used for all periods where no rate is entered. If a reset table that only contained the first 2 reset periods is used, the function will add one extra reset period from the last given terminating date to the maturity date, and the last rate given will apply to the additional period. Thus, a reset table consisting of only the first two periods will give the same results as the table shown.

Fixed Payment Table

payment date	fixed payment amount
1-Jul-2007	100,000

The function aaFRNavg_FixFwds_fs_cf can be called using the above tables, and the inputs below, to calculate the cash flows, as well as output a reset table showing the rate used, the notional amount, interest, and accrued interest for each reset period.

Argument	Description	Example Data	Switch
d_v	value (settlement) date	5-Feb-2005
payperiod	pay periods	see above
npa_tbl	notional table	see above
reset_tbl	reset table	see above
flleg_fixpay	fixed payment table	see above
acc_pay	accrual method for coupon payments	1	actual/365 (fixed)
position	trade position	1	long
table_type	table type	1,2,3	cash flow, reset, and interest summary tables

Results: Cash Flow Table (table_type = 1)

date	interest	principal payment	total cash flow	accrued interest
1-Apr-2005	1,232.88	0	1,232.88	479.45
1-Jul-2005	1,246.58	0	1,246.58	0
1-Oct-2005	1,386.30	0	1,386.30	0
1-Jan-2006	1,386.30	0	1,386.30	0
1-Apr-2006	1,356.16	0	1,356.16	0
1-Jul-2006	1,371.23	0	1,371.23	0
1-Oct-2006	1,386.30	0	1,386.30	0
1-Jan-2007	1,386.30	0	1,386.30	0
1-Apr-2007	1,356.16	0	1,356.16	0
1-Jul-2007	1,371.23	100,000	101,371.23	0

Results: Reset Table (table_type = 2)

payment date	reset date	effective date	terminating date	notional	rate	rate + mgn	weight	interest	accrued
1-Apr-2005	1-Jan-2005	1-Jan-2005	1-Feb-2005	100,000	5.0%	5.0%	8493	424.66	424.66
1-Apr-2005	1-Jan-2005	1-Feb-2005	1-Apr-2005	100,000	5.0%	5.0%	16164	808.22	54.79
1-Jul-2005	1-Jan-2005	1-Apr-2005	1-Jul-2005	100,000	5.0%	5.0%	24932	1,246.58	0
1-Oct-2005	1-Jul-2005	1-Jul-2005	1-Oct-2005	100,000	5.5%	5.5%	25205	1,386.30	0
1-Jan-2006	1-Jul-2005	1-Oct-2005	1-Jan-2006	100,000	5.5%	5.5%	25205	1,386.30	0
1-Apr-2006	1-Jan-2006	1-Jan-2006	1-Apr-2006	100,000	5.5%	5.5%	24658	1,356.16	0
1-Jul-2006	1-Jan-2006	1-Apr-2006	1-Jul-2006	100,000	5.5%	5.5%	24932	1,371.23	0
1-Oct-2006	1-Jul-2006	1-Jul-2006	1-Oct-2006	100,000	5.5%	5.5%	25205	1,386.30	0
1-Jan-2007	1-Jul-2006	1-Oct-2006	1-Jan-2007	100,000	5.5%	5.5%	25205	1,386.30	0
1-Apr-2007	1-Jan-2007	1-Jan-2007	1-Apr-2007	100,000	5.5%	5.5%	24658	1,356.16	0
1-Jul-2007	1-Jan-2007	1-Apr-2007	1-Jul-2007	100,000	5.5%	5.5%	24932	1,371.23	0

Results: Interest Summary Table (table_type = 3)

payment date	avg cpn	interest	accrued
1-Apr-2005	5.000%	1,232.88	479.45
1-Jul-2005	5.000%	1,246.58	0
1-Oct-2005	5.500%	1,386.30	0
1-Jan-2006	5.500%	1,386.30	0
1-Apr-2006	5.500%	1,356.16	0
1-Jul-2006	5.500%	1,371.23	0
1-Oct-2006	5.500%	1,386.30	0
1-Jan-2007	5.500%	1,386.30	0
1-Apr-2007	5.500%	1,356.16	0
1-Jul-2007	5.500%	1,371.23	0

The function aaFRNavg_FixFwds_fs_p can be used to calculate the price of the FRN given a yield and the rate basis of that yield. Several risk statistics are also calculated, including Duration, Modified Duration, Convexity, and Basis Point Value.

aaFRNavg_FixFwds_fs_p

Argument	Description	Example Data	Switch
d_v	value (settlement) date	5-Feb-2005
payperiod	pay periods	see above
npa_tbl	notional table	see above
reset_tbl	reset table	see above
flleg_fixpay	fixed payment table	see above
yield	yield to maturity	4.65%
yield_basis	rate basis of yield to maturity	3	quarterly
acc_pay	accrual method for coupon payments	1	actual/365 (fixed)
position	trade position	1	long
stat	statistic	{1, 2, …, 9}

Results

Statistic	Description	Value
1	fair value	101,721.14
2	accrued interest	479.45
3	value of future cash flows (fair value + accrued)	102,200.59
4	duration	2.259791
5	modified duration	2.233822
6	convexity	0.279005
7	basis point value	-4.1917
8	number of days of accrued interest	35
9	effective duration	0.410158

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