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

{\displaystyle P\times \sum _{i=1}^{N}1_{{\text{index}}(i)\in {\text{Range}}}\times {\frac {1}{N}}}

  • 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%.

Other products

Spread Range Accrual Note

A range note in which the coupon depends on the spread between the daily fixings of two interest rate indexes being within a specific range. For example, the spread may be based on the LIBOR-CMS differential. This note is attractive to investors at times the market is expected to see wide movements in the underlying spread. The coupon goes hand in hand with the volatility of the spread and the possibility of it sliding outside the range.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s