In finance, the accrual range is a type of derivative product that is very popular among structured note investors. It is estimated that over US $ 160 billion of the Indexed Range Accrual at interest rates has only been sold to investors between 2004 and 2007. This is one of the most popular non-vanilla financial derivatives. In essence, investors in the accrual range are betting that the "index" reference - usually the interest rate or exchange rate - will remain within a predetermined range.
Video Range accrual
Payoff description
Express umum untuk hasil dari rentang akrual adalah:
- index ( i ) adalah nilai indeks pada tanggal observasi i th
- N adalah jumlah total pengamatan dalam suatu periode
- P adalah pembayaran saat indeks berada dalam rentang
Jika frekuensi observasi setiap hari, imbalannya bisa lebih mudah ditulis sebagai
Where
- n is the number of days of a given index within the given range
- N is the number of days from the observation period
- P is a payment for a given day when the index is in the range
An index can be an interest rate (eg Libor USD 3 months), or an FX exchange rate (eg EUR/USD) or a commodity (eg oil price) or other observable financial index.
Observation periods may vary from daily (eg Weekly, monthly, etc.), although daily observations are the most common.
The recipient of various accrued coupons sells binary options. The value of this option is used to increase the paid coupon.
Example
Let's take the example of a 5-year accrual record related to a USD 3 month Libor, with the range set as [1.00%; 6.00%] and a conditional coupon of 5.00%. Let's assume the record begins on January 1, 2009 and the first coupon payment will occur on July 1, 2009.
An investor who buys USD 100 million from this note will have the following cash flows:
- First coupon - Between 1 January and 1 July 2009, if USD 3 million Libor fix between
1.00% and 6.00% for 130 days, the tariff applied for the first semester is:
- 5,00% ÃÆ'â € "130/181 = 3,5912% (total there are 181 days between 1 January 2009 and 1 July 2009) .
- The coupon paid on July 1, 2009 will be: US $ 100mÃ, ÃÆ'â € "Ã, 3,5912% Ã, ÃÆ' â €" 0.5 = $ 1,795,600 (assuming 0.5 for the calculation fraction days between January 1, 2009 and July 1, 2009)
- Second voucher - Between 1 July 2009 and 1 January 2010, if USD 3 million Libor fix between 1.00% and 6.00% for 155 days, then the tariff applied for the second semester is:
- 5.00% ÃÆ'â € "155/184 = 4,2120%.
- Coupons paid on January 1, 2010 are: US $ 100mÃ, ÃÆ'â € "Ã, 4,2120% Ã, ÃÆ' â €" 0.5 = $ 2,106,000 (assuming 0.5 for the calculation fraction days between July 1, 2009 and January 1, 2010) .
- For the following 8 coupons, the same methodology applies. The highest rate investors will get is 5.00% and 0.00%.
- Damiano Brigo, Fabio Mercurio (2001). Interest Rate Model - Theory and Practice with Smiles, Inflation and Credit (2nd ed. 2006 ed.). Springer Verlag. ISBN: 978-3-540-22149-4.
Different types of accrual range
Payments ( P in our notation), because every day the index is in range, can be either an improvement or variable level.
Maps Range accrual
Rating and risk
Accrual range can be seen as a binary option strip, with a lag that decreases between the assignment date and the payment date. For this reason, it is important that the rating model be well calibrated to the underlying volatility term structure, at least to the strike implied by the range.
If further accrual ranges can be called, then the assessment model also needs to take into account the dynamics between swaption and underlying.
Accrual swaps that monitor the permanent interest rate into the range and pay the associated interest rate multiplied by the immortality factor also depend on the correlation at various adjacent advanced levels. For details see for example Brigo and Mercurio (2001).
Market
(To complete)
References
Source of the article : Wikipedia
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