Valuing, hedging, and managing the risk of structured deposits and structured notes sometimes involves interest rate products with more complex terms than interest rate swaps or caps.

How they differ from standard rate derivatives

The standard interest rate derivatives are the FRA, interest rate futures, the interest rate swap, the cap and floor, and the European swaption. Products with more complex terms than these are called interest rate exotics. A 1998 US Federal Reserve manual says that many exotic options are traded as OTC derivatives, and that their markets are less liquid than those for standard options1.

The six products in this chapter fall into the three groups in the table below, based on how they differ from standard products.

What differs from standard products Products Closest standard products
The right can be exercised on more than one date, not only at expiry Bermudan swaptions, callable swaps European swaptions
The reference rate is a long-term swap rate CMS, CMS spread options Interest rate swaps, caps and floors
Coupons depend on conditions or on past coupons Range accruals, snowballs Floating-rate notes

This grouping is for explanation only, and actual products may combine several of these features. One example is a note whose coupon rises when short-term rates fall, with a right for the issuer to redeem it early on each interest payment date and a guarantee that keeps the coupon at 0% or above2.

Products with more than one exercise date

The Bermudan Swaptions page covers the Bermudan swaption, an option to enter into an interest rate swap on any one of several dates set in advance. An option that can be exercised on several dates is called a Bermudan option. Bermudan swaptions can be used for purposes such as hedging structured deposits with several early redemption dates3.

A callable swap is a swap in which one party holds the right, in exchange for a premium, to terminate the interest rate swap early. The US Federal Reserve manual counts it as a type of swaption4.

Products that reference a long-term swap rate

A CMS (constant maturity swap) is an interest rate swap that references a swap rate as its floating rate5. For example, it periodically exchanges a short-term rate, such as a 1-year rate, for a long-term rate, such as the 10-year swap rate6.

A CMS spread option is an option on the difference between two swap rates of different tenors. An option whose payoff is set by comparing the difference between the prices of two underlying assets with the strike price is called a spread option, and long-term and short-term rates are given as an example of the underlying assets7. "Steepener" notes pay a relatively high coupon for the first year, after which the coupon is set by the slope of the yield curve (the difference between long-term and short-term rates). The US Financial Industry Regulatory Authority (FINRA) gives them as an example of a complex product8.

Products whose coupons depend on conditions or past coupons

A range accrual accrues interest at a higher rate on days when the reference rate is inside a range set in advance and at a lower rate (sometimes 0%) on days when it is outside. An investor who buys a note of this kind is in the same position as having sold a series of digital options struck at the upper and lower ends of the range9.

A snowball sets each period's coupon from the previous period's coupon and a floating rate. Snowball notes are an example of a product whose payoff depends on past interest rates10. Each coupon depends not only on the rate at that time but also on how rates have moved up to then, so the product is path-dependent.

Why they are embedded in structured products

Interest rate exotics are sometimes traded as part of structured products. A structured product combines a loan, deposit, or bond with swaps or options. Many of these products aim for a higher yield by having the investor sell options and receive the premium, or by applying leverage to the coupon11. Most options embedded in US structured notes are caps, floors, and early redemption rights sold by the investor to the issuer12. How to view bonds and deposits as combinations with derivatives is covered in What Are Structured Products?.

InvestorIssuerCounterpartyTo the swapPrincipalCoupon1y LIBOR + α10y swap rate
Figure 1Cover trade between the issuer of a CMS note and its swap counterparty
Figure description

The payments among the investor, the issuer, and the swap counterparty, based on the CMS note example in a Bank of Japan document on structured products. The investor pays the principal to the issuer and receives from the issuer a coupon equal to the 10-year swap rate minus α. α is an adjustment margin that reflects factors such as the level of market rates and the creditworthiness of the parties. The issuer pays the swap counterparty 1-year LIBOR plus α and receives the 10-year swap rate from the swap counterparty. The issuer funds the part of the investor's coupon that is linked to the 10-year swap rate with what it receives from the swap counterparty.

As Figure 1 shows, the issuer receives from the swap counterparty the 10-year swap rate on which the investor's coupon is based. This trade between the issuer and the swap counterparty is called a cover trade. The guarantee that keeps the coupon at 0% or above (a zero floor) is also bought by the investor from the issuer, and the issuer buys a floor of the same form from the swap counterparty13. The 1-year LIBOR in the figure is an example from the time of the document.

For the investor, the yield rises if rates move in the direction the product assumes and falls if they move the other way. In the CMS note in the Bank of Japan document, the coupon increases when long-term rates rise. However, if the yield curve rises and flattens, the price of the note falls, and the margin over the investor's funding cost may narrow or turn negative14. According to the US Federal Reserve manual, a range accrual note yields more than other floating-rate notes if rates stay stable within the range, and less if rates move sharply outside it15.

Why valuation and risk management are difficult

Most derivatives have no closed-form price, so prices are generally computed with numerical methods such as Monte Carlo simulation. Accuracy and speed of calculation, however, generally cannot both be achieved16. A 2010 paper by the Bank of Japan's Institute for Monetary and Economic Studies says that in practice, interest rate options are often priced with a term structure model, which describes how the yield curve moves. According to the paper, as the number of trades grows and product maturities lengthen, there is demand to lighten the computational load of such models and to make the calculations more stable. The LIBOR market model (LMM), a term structure model widely used in practice at the time of the paper, has the following issues17.

  • It is often implemented with Monte Carlo simulation, which makes the computational load relatively heavy.
  • Valuing a right that can be exercised before maturity requires computational techniques such as least-squares Monte Carlo. This adds to the load, and depending on the regression equation used in the calculation, the computed price is prone to bias.
  • When market volatility differs by strike price (when there is a smile), fitting the model to market prices becomes more complex.

In the same paper's tests, a lognormal LIBOR market model and a single-factor Markov functional model, fitted to the same market data, did not necessarily give the same computed price for a Bermudan swaption. The difference in valuation between the two models is described as small enough to be acceptable in practice. In the setting with a smile, it is not easy to verify rigorously whether the level of the computed price is accurate18.

A CMS requires what is called a convexity adjustment. This is because the expected swap rate at the payment date generally differs from the forward swap rate implied by today's market19. Products with more than one underlying asset, such as CMS spread options, are affected by the correlation between the underlying assets. This correlation risk is a risk that products with a single underlying asset do not have20.

On the trading side, many structured products have quite illiquid markets. A sale is not always possible, and the actual sale price may be well below the theoretical price21.

The order in which to read this chapter

Each page in this chapter builds on the pages on interest rate swaps, swap valuation, caps and floors, and swaptions. After that, reading in the following order within each group of the table lets each page build on the one before. For products with more than one exercise date, read Bermudan swaptions first and callable swaps second. For products that reference a long-term swap rate, read CMS first and CMS spread options second. Range accruals and snowballs can be read in either order. You can move to each page from the related pages below.

Notes

  1. Board of Governors of the Federal Reserve System, "Trading and Capital-Markets Activities Manual," Section 4330.1 "Options," "Exotic Options" (page dated February 1998, page 2). ↩

  2. Bank of Japan, Financial System and Bank Examination Department, Center for Advanced Financial Technology, "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), page 6, the worked example in "（２）リバース・フローター債" ((2) Reverse floater notes) (the zero floor and the multi-callable feature) (in Japanese). ↩

  3. Haruyasu Ota, "マルコフ関数モデルによる金利オプションの価格付けの実用化" (Putting the Markov-functional model into practice for pricing interest rate options), Kinyu Kenkyu, Institute for Monetary and Economic Studies, Bank of Japan (October 2010), page 133, note 3 (in Japanese). ↩

  4. Board of Governors of the Federal Reserve System, "Trading and Capital-Markets Activities Manual," Section 4340.1 "Swaptions," "Cancelable Swaps" (page dated February 1998, page 1). ↩

  5. Keiichi Tanaka, Takeshi Yamada, and Toshiaki Watanabe, "金利派生商品の効率的な価格付け：確率密度関数の近似を用いて" (Efficient pricing of interest rate derivatives using approximations of the probability density function), Kinyu Kenkyu, Institute for Monetary and Economic Studies, Bank of Japan (October 2006), page 9, "（1）CMS" ((1) CMS) (in Japanese). ↩

  6. Bank of Japan, Financial System and Bank Examination Department, Center for Advanced Financial Technology, "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), page 8, "（3）CMS（constant maturity swap＊）債" ((3) CMS (constant maturity swap) notes) (in Japanese). ↩

  7. Kazutaka Nakamura, "相関デリバティブのリスク特性やリスク管理手法に関する考察" (A study of the risk characteristics and risk management methods of correlation derivatives), Institute for Monetary and Economic Studies, Bank of Japan, Discussion Paper No. 2003-J-7, page 3, "スプレッド･オプション" (Spread options) (in Japanese). ↩

  8. FINRA, "Regulatory Notice 12-03" (January 2012), page 4, the examples of complex products. ↩

  9. Board of Governors of the Federal Reserve System, "Trading and Capital-Markets Activities Manual," Section 4040.1 "Structured Notes," "Range Notes" (page dated February 1998, pages 4–5). ↩

  10. Haruyasu Ota, "マルコフ関数モデルによる金利オプションの価格付けの実用化" (Putting the Markov-functional model into practice for pricing interest rate options), Kinyu Kenkyu, Institute for Monetary and Economic Studies, Bank of Japan (October 2010), page 136, note 9 (in Japanese). ↩

  11. Bank of Japan, Financial System and Bank Examination Department, Center for Advanced Financial Technology, "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), page 3, "１．仕組商品とは" (1. What structured products are) (in Japanese). ↩

  12. Board of Governors of the Federal Reserve System, "Trading and Capital-Markets Activities Manual," Section 4040.1 "Structured Notes," "General Description" (page dated March 1999, page 1). ↩

  13. Bank of Japan, Financial System and Bank Examination Department, Center for Advanced Financial Technology, "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), page 9, "基本的な仕組み［CMS債］" (Basic structure [CMS notes]) (in Japanese). ↩

  14. Bank of Japan, Financial System and Bank Examination Department, Center for Advanced Financial Technology, "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), pages 8 and 10, "ＣＭＳ債のリスク特性" (Risk characteristics of CMS notes) (in Japanese). ↩

  15. Board of Governors of the Federal Reserve System, "Trading and Capital-Markets Activities Manual," Section 4040.1 "Structured Notes," "Range Notes" (page dated February 1998, page 5). ↩

  16. Keiichi Tanaka, Takeshi Yamada, and Toshiaki Watanabe, "金利派生商品の効率的な価格付け：確率密度関数の近似を用いて" (Efficient pricing of interest rate derivatives using approximations of the probability density function), Kinyu Kenkyu, Institute for Monetary and Economic Studies, Bank of Japan (October 2006), page 2, "１．はじめに" (1. Introduction) (in Japanese). ↩

  17. Haruyasu Ota, "マルコフ関数モデルによる金利オプションの価格付けの実用化" (Putting the Markov-functional model into practice for pricing interest rate options), Kinyu Kenkyu, Institute for Monetary and Economic Studies, Bank of Japan (October 2010), page 132, "1. はじめに" (1. Introduction) (in Japanese). ↩

  18. The same paper, pages 163–164, "イ. キャプレットにフィッティングした場合" (b. When fitted to caplets) and the explanation after Tables 10 and 11. ↩

  19. Keiichi Tanaka, Takeshi Yamada, and Toshiaki Watanabe, "金利派生商品の効率的な価格付け：確率密度関数の近似を用いて" (Efficient pricing of interest rate derivatives using approximations of the probability density function), Kinyu Kenkyu, Institute for Monetary and Economic Studies, Bank of Japan (October 2006), pages 2 and 10 (in Japanese). ↩

  20. Kazutaka Nakamura, "相関デリバティブのリスク特性やリスク管理手法に関する考察" (A study of the risk characteristics and risk management methods of correlation derivatives), Institute for Monetary and Economic Studies, Bank of Japan, Discussion Paper No. 2003-J-7, page 1, "１．はじめに" (1. Introduction) (in Japanese). ↩

  21. Bank of Japan, Financial System and Bank Examination Department, Center for Advanced Financial Technology, "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), page 30, "（１）購入前の検討（続き）" ((1) Considerations before buying, continued) (in Japanese). ↩

  22. Bank of Japan, Financial System and Bank Examination Department, Center for Advanced Financial Technology, "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), pages 29 and 34, "４．リスク管理のポイント" (4. Key points of risk management) (in Japanese). ↩