Digital Coupon Notes

When you explain a structured note to a customer, or check its risk by scenario before purchase, the amount received on each determination date takes one of two forms: a fixed amount, or zero (or a lower rate). Check both with a graph or table.

A bond whose coupon depends on the level on the determination date

In the Japan Securities Dealers Association document, a "Nikkei Stock Average-linked note with a floating interest rate" applies a high interest rate if the Nikkei Stock Average on the rate-setting date is at or above a reference price, and a low rate if it is below¹. This form, that is, a structured note whose coupon is set high or low by the level of an index or similar reference on the determination date, is called a digital coupon note. The issuer pays the coupon to the investor. The general way of splitting a structured note into a bond and options is covered in What Are Structured Products?.

Consider a hypothetical example in which Company H issues a digital coupon note that references the Nikkei Stock Average. The terms are as follows.

• The face value is 1 million yen and the term is 3 years.
• The determination dates are once a year, at 1, 2, and 3 years, and the coupon is paid on each determination date.
• The reference price is 10,000 yen. If the Nikkei Stock Average on a determination date is at or above 10,000 yen, a coupon of 4% of face value (40,000 yen) is paid. If it is below 10,000 yen, the coupon is 0 yen.
• At maturity, the face value of 1 million yen is redeemed. This assumes, however, that the issuer is able to pay (see the section "The issuer's credit and the risk of selling early" below).

Setting the lower rate at 0% is a choice made in this example. Some range notes referenced indexes linked to interest rates, currencies, commodities, and equities, and a 1998 document says some had a lower rate of 0%².

Figure description

The investor pays 1 million yen to Company H at issue. Company H pays the investor a coupon of 40,000 yen only if the Nikkei Stock Average on a determination date is at or above 10,000 yen. At maturity, Company H pays the investor the face value of 1 million yen.

The amount received on each determination date

The coupon on each determination date is either 40,000 yen or zero. How far the Nikkei Stock Average on a determination date is above 10,000 yen does not change the coupon. As a comparison, take an ordinary fixed-rate bond with the same term (in this example, 2% a year, a coupon of 20,000 yen each year). The amounts received in three cases are as follows.

In case A the average is at or above the reference price on all 3 dates, so the coupons total 120,000 yen, 60,000 yen more than the ordinary bond. In case B the average is 9,900 yen only at year 2, and the coupons total 80,000 yen. Even so, this is 20,000 yen more than the ordinary bond. In case C the average is below the reference price on all 3 dates, so there are no coupons at all, and the total at maturity stays at the face value of 1 million yen. That is 60,000 yen less than an ordinary bond of the same term. The note comes out ahead of the ordinary bond when the condition is met on 2 or more dates (with the figures in this example).

Figure description

The cash flows of case B in the table, drawn from the investor's side. The investor pays 1 million yen at issue. At year 1 the Nikkei Stock Average is 10,200 yen, at or above the reference price, so the investor receives a coupon of 40,000 yen. At year 2 it is 9,900 yen, below the reference price, so nothing is received. At year 3 it is 10,100 yen, at or above the reference price, so the investor receives the coupon of 40,000 yen plus the face value of 1 million yen, 1.04 million yen in total. The length of each arrow is a rough guide to the amount.

Splitting into a zero-coupon bond and digital options

A digital coupon note can be viewed as a zero-coupon bond that pays face value at maturity plus a digital option for each determination date. A zero-coupon bond is a bond that pays no coupons and is issued at a price below face value⁶. Structured products are products built by combining swaps or options with ordinary bonds and similar instruments⁷. A digital option is an option under which, depending on whether the price at maturity is beyond the strike price, a fixed amount is received or nothing is received⁸.

In Company H's example, the 1 million yen the investor pays at issue is viewed as going to the following two things.

• A 3-year zero-coupon bond paying 1 million yen at maturity. Let the price of Company H's zero-coupon bond be 940,000 yen.
• For each determination date at 1, 2, and 3 years, a digital call (strike price 10,000 yen) that pays 40,000 yen if the Nikkei Stock Average is at or above 10,000 yen. The remaining 60,000 yen goes toward the price of the 3 digital calls and Company H's costs.

The lower the price of the zero-coupon bond, the more can be spent on the digitals. For the same price of the digitals, the harder the determination-date condition is to meet, the higher the coupon can be when it is met.

Seen another way, Company H issues a bond that always pays 40,000 yen on each determination date, and the investor makes a promise to Company H to hand back 40,000 yen when the level on the determination date is below the reference price (selling a digital put). A digital call and a digital put, each paying a fixed amount or nothing, add up, except exactly at the strike price, to a fixed amount whatever the price at maturity (this follows from the definitions). So not paying the coupon when the level is below the reference price is the same as the investor selling a digital put.

In the type in which a lower rate, rather than 0, is paid when the condition is not met, the amount of the put the investor sells is the difference between the coupon at the high rate and the coupon at the low rate. The price of a digital option is found as the discounted expected value of its payoff⁹. The definition and valuation of digital options and what changes their value are covered in Digital Options.

A small move at the boundary changes the coupon a lot

Whether the level on a determination date is just above or just below the reference price changes the whole of one coupon. In Company H's example, the coupon for each Nikkei Stock Average level on a determination date is as follows.

The difference between 9,999 yen and 10,000 yen is 1 yen, but the coupon changes by 40,000 yen. Between 10,000 yen and 12,000 yen, the level is 20% different, yet the coupon is the same. How a date on which the level is exactly the reference price is treated depends on how the condition is written. Even in definitions of digital options, some sources write "beyond"⁸ and others write "at or above"¹⁰. The example above uses the "at or above the reference price" form shown by the Japan Securities Dealers Association¹.

The number of determination dates is also set by the terms of the bond. In the 1998 document, most range notes checked the reference level daily, and there were also forms that checked monthly, quarterly, or only once during the term². For a digital coupon note too, the fewer the determination dates, the larger the share of the amount received that rides on a single determination. If there is only one determination date, the level on that day alone decides whether a coupon is paid.

The issuer's credit and the risk of selling early

If the issuer's financial condition worsens, payments of principal or interest may be delayed and the price of the bond may fall¹¹. In Company H's example, even when the condition is met and a coupon is due, if Company H cannot pay, neither the coupon nor the face value is received.

The price when selling before maturity is also a risk. A Nikkei Stock Average-linked note can be hard to sell before maturity, and if sold before maturity, the sale price may be below face value¹². The more complex a structured note is, the more limited the buyers, and selling before maturity can mean a large loss¹³. The Bank of Japan document asks readers to expect that the sale price may be considerably lower than the theoretical price¹⁴.

For a note in a foreign currency, movements in the exchange rate can make the amount received in yen fall below the amount invested¹⁵. In a form like this example, where face value is redeemed at maturity, a loss comes from the loss of coupons and from these risks.

Differences from similar notes

A note whose coupon is set by a condition and a note whose redemption amount is set by a condition differ in where the condition enters the payment. The knock-in type, in which the redemption amount itself changes with the index, is covered in Equity Index-Linked Notes.

A digital coupon note is decided by the full amount or zero on each determination date. A range accrual checks whether the level is within the range mostly daily (monthly and quarterly forms also existed in the 1998 document), so the interest varies with the number of days spent within the range. In the same document, a range note accrued interest at a high rate during the period when the level was within the range². With a knock-in type, if the level falls during the observation period, the redemption amount changes in line with the movement of the share price¹.

Notes

1. Japan Securities Dealers Association, "日経平均リンク債の特徴やリスクとは？" (What are the features and risks of Nikkei Stock Average-linked notes?, in Japanese), page 1, "１．そもそも日経平均リンク債とは？" (1. What is a Nikkei Stock Average-linked note?), the parts on notes with a floating interest rate and notes with a floating redemption amount. ↩ ↩² ↩³

2. Board of Governors of the Federal Reserve System, "Trading and Capital-Markets Activities Manual" (February 1998), Section 4040.1, "Structured Notes," page 4, "Range Notes." ↩ ↩² ↩³

3. Japan Securities Dealers Association, "日経平均リンク債の特徴やリスクとは？" (in Japanese), page 3, note on "利率（クーポン）" (interest rate (coupon)). ↩

4. Japan Securities Dealers Association, "日経平均リンク債の特徴やリスクとは？" (in Japanese), page 2, "説明を受けるべき事項" (Matters to be explained). ↩

5. Center for Advanced Financial Technology, Financial System and Bank Examination Department, Bank of Japan, "仕組商品投資のリスク把握と管理" (Understanding and managing the risks of investing in structured products, in Japanese), page 15, "３．シナリオ分析" (3. Scenario analysis). ↩

6. Board of Governors of the Federal Reserve System, "Trading and Capital-Markets Activities Manual" (February 1998), Section 4045.1, "Corporate Notes and Bonds," page 2, "Zero-Coupon Bonds." ↩

7. Center for Advanced Financial Technology, Financial System and Bank Examination Department, Bank of Japan, "仕組商品投資のリスク把握と管理" (in Japanese), page 3, "１．仕組商品とは" (1. What structured products are). ↩

8. Durham University, Department of Mathematical Sciences, "Chapter 5 Pricing options from around the world (Mathematical Finance Lecture Notes 2024-25)," the paragraph defining digital (binary) options. A cash-or-nothing call pays a fixed amount if the price at maturity is above the strike price, and a put pays it if the price is below. ↩ ↩²

9. The same source, the paragraph explaining risk-neutral valuation. The discounted expected value of the payoff is the value at time 0. ↩

10. Board of Governors of the Federal Reserve System, "Trading and Capital-Markets Activities Manual" (February 1998), Section 4040.1, "Structured Notes," page 4, "Range Notes," footnote 1. ↩

11. Japan Securities Dealers Association, "日経平均リンク債の特徴やリスクとは？" (in Japanese), page 3, note on "発行者の信用リスク" (issuer's credit risk). ↩

12. Japan Securities Dealers Association, "日経平均リンク債の特徴やリスクとは？" (in Japanese), page 7. ↩

13. Board of Governors of the Federal Reserve System, "Trading and Capital-Markets Activities Manual" (February 1998), Section 4040.1, "Structured Notes," page 8, "Liquidity Risk." ↩

14. Center for Advanced Financial Technology, Financial System and Bank Examination Department, Bank of Japan, "仕組商品投資のリスク把握と管理" (in Japanese), page 30, "（１）購入前の検討（続き）" (1. Review before purchase (continued)). ↩

15. Japan Securities Dealers Association, "日経平均リンク債の特徴やリスクとは？" (in Japanese), page 6, "日経平均リンク債に特有のリスク" (Risks specific to Nikkei Stock Average-linked notes). ↩