# Product ABC (1): Range Accrual

When reading an article about the financial crisis during the 2007-2008, there is one special product draws my attention – Range Accrual. I may take this chance to deeply look into this product and analyze this interesting product

## Payoff description

• index(i) is the value of the index at the ith observation date
• N is the total number of observations within a period
• P is the payout when the index is in the range

## Example

Let’s take an example of a 5 years range accrual note linked to USD 3 months Libor, with range set as [1.00%; 6.00%] and a conditional coupon of 5.00%. Let’s assume the note to start on January 1, 2009 and the first coupon payment to happen on July 1, 2009.

An investor who buys USD 100m of this note will have the following cash flows:

• First coupon — Between January 1 and July 1, 2009, if USD 3m Libor fixes between

1.00% and 6.00% for 130 days, then the rate applied for the first semester will be:

5.00% × 130/181 = 3.5912% (there are 181 days in total between January 1, 2009 and July 1, 2009).
The coupon paid on July 1, 2009 would be: US$100m × 3.5912% × 0.5 =$1,795,600 (assuming 0.5 for the day-count fraction between January 1, 2009 and July 1, 2009)
• Second coupon – Between July 1, 2009 and January 1, 2010, if USD 3m Libor fixes between 1.00% and 6.00% for 155 days, then the rate applied for the second semester will be:
5.00% × 155/184= 4.2120%.
The coupon paid on January 1, 2010 would be: US$100m × 4.2120% × 0.5 =$2,106,000 (assuming 0.5 for the day-count fraction between July 1, 2009 and January 1, 2010).
• For the 8 following coupons, the same methodology applies. The highest rate investor will get is 5.00% and the lowest 0.00%.