Corporate bonds pricing

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An example of a two-factor RF model could e.g. be enforced by a separate modeling of bond prices for corporate bonds and default spreads. 

However, a critical issue on this spread measure is how the asset swap has been stmctured. ASW measure works very well when bond prices trade at or near to par. Most corporate bonds trade with price away from the par (as in this case), thus making the ASW an inaccurate spread measure. If the bond trades at premium, the ASW spread will overestimate the level of credit risk conversely, if the bond trades at discount the ASW spread will underestimate the level of credit risk. Therefore, in the case of HERIM and TKAAV, the ASW spread overestimates the credit risk associated with the bonds because both trade significantly at premium. 

A credit default swap (CDS) price provides fundamental credit risk information of a specific reference entity or asset. As explained before, asset swaps are used to transform the cash flows of a corporate bond for interest rate hedging purpose. Since the asset swaps are priced at a spread over the interbank rate, the ASW spread is the credit risk of the same one. However, market evidence shows that credit default swaps trade at a different level to asset swaps due to technical... 

Central banks and market practitioners use interest rates prevailing in the government bond market to extract certain information, the most important of which is implied forward rates. These are an estimate of the market s expectations about the future directirMi of short-term interest rates. They are important because they signify the market s expectafirMis about the future path of interest rates however, they are also used in derivative pricing and to create synthetic bond prices from the extent of credit spreads of corporate bonds. 

The general rule of corporate bonds is that they are priced at a spread to the government yield curve. In absolute terms, the yield spread is the difference between the yield to maturity of a corporate bond and the benchmark, generally a yield to maturity of a govermnent bond with the same maturity. Corporate bonds include a yield spread on a risk-free rate in order to compensate two main factors, liquidity premium and credit spread. The yield of a corporate bond can be assumed as the sum of parts of the elements as shown in Figure 8.1, in which the yield spread relative to a default-free bond is given by the sum of default premium (credit spread) and liquidity premium. 

Z-spread The Z-spread or zero volatility spread calculates the yield spread of a corporate bond by taking a zero-coupon bond curve as benchmark. Conversely to other yield spreads, the Z-spread is constant. In fact, it is found as an iterative procedure, which is the yield spread required to get the equivalence between market price and the present value of all its cash flows. The Z-spread is given by Equation (8.2) ... 

The price of a corporate bond is a yield spread for conventional bonds or on an OAS basis for callable or other option-embedded bonds. If an OAS calculation is undertaken in a consistent framework, price changes that result in credit events will result in changes in the OAS. Therefore, we can speak in terms of a sensitivity measure for the change in value of a bond or portfolio in terms of changes to a... 

This means that p f) is the expected value of the present value of the bond s cash flows, that is, the expected yield gained by buying the bond at the price p f) and holding it to maturity is r. If our required yield is r, for example this is the yield on the equivalent-maturity government bond, then we are able to determine the coupon rate C for which p r) is equal to 100. The default-risk spread that is required for a corporate bond means that C will be greater than r. Therefore, the theoretical default spread is C — r basis points. If there is a zero probability of default, then the default spread is 0 and C = r. 

As shown in previous sections, the credit spread on a corporate bond takes into account its expected default loss. Structural approaches are based on the option pricing theory of Black Scholes and the value of debt depends on the value of the underlying asset. The determination of yield spread is based on the firm value in which the default risk is found as an option to the shareholders. Other models proposed by Black and Cox (1976), Longstaff and Schwartz (1995) and others try to overcome the limitation of the Merton s model, like the default event at maturity only and the inclusion of a default threshold. This class of models is also known as first passage models . 

Duffee, G.R., 1996b. Estimating the Price of Default Risk. Federal Reserve Board, Washington, DC. Duffee, G.R., 1998. The relation between treasury yields and corporate bond yield spreads. J. Financ. 53 (6), 2225-2241. 

As noted, the share price is a key parameter of the option pricing model. An increase in the underlying share price will result in a rise of the convertible price, and a decrease in the share price will result in a fall of the convertible price. Figure 9.9 illustrates the comparison between the convertible bond price and share price of Intel Corporation. 

The most actively traded government securities for various maturities are called benchmark issues. Yields on these issues serve as reference interest rates which are used extensively for pricing other securities. Exhibit 1.2 is a Bloomberg screen of the benchmark bonds issued by the government of the Netherlands. European government bonds will be discussed in Chapter 5. As an illustration of a corporate bond. Exhibit 1.3 shows a Bloomberg Security Description screen for 4.875% coupon bond issued by Pirelli SPA that matures on 21 October 2008. 

The minimum interest rate that an investor should require is the yield available in the marketplace on a default-free cash flow. For bonds whose cash flows are denominated in euros, yields on European government securities serve as benchmarks for default-free interest rates. In some European countries, the swap curve serves as a benchmark for pricing spread product (e.g., corporate bonds). For now, we can think of the minimum interest rate that investors require as the yield on a comparable maturity benchmark security. 

The CCABS market continues to be a safe haven for European ABS investors. Especially in 2002, when corporate bonds of various sectors showed increased price volatility and the CDO market experienced a significant number of downgrades, credit card ABS transactions continued to show strong and stable performance. In fact, since the market s inception in 1995, no European CCABS have experienced any downgrades. We believe that CCABS are likely to continue to exhibit strong and stable performance and remain one of the core asset classes for European ABS investors. 

Exhibit 21.4 illustrates a generic TR swap. The protection buyer has contracted to pay the total return on a specified reference asset, while simultaneously receiving a LIBOR-based return from the protection seller. The reference or underlying asset can be a bank loan such as a corporate loan or a sovereign or corporate bond. The total return payments include the interest payments on the underlying loan as well as any appreciation in the market value of the asset. The protection seller will pay the LIBOR-based return it will also pay any difference if there is a depreciation in the price of the asset. The economic effect is as if this entity owned the underlying asset, as such TR swaps are synthetic loans or securities. 

Corporate bonds are less frequently traded than Treasury bonds. Thus stale prices can contribute to the lower volatility of corporates. 

The number and size of fallen angels in the recent past show the importance of independent buy-side research. Internal ratings might help investors to generate investment decisions which avoid fallen angels or to sell their exposure early enough before the corporate bond s price deteriorates. Furthermore, quantitative models have helped us to react very quickly to relevant information such as an announced debt financed takeover to adjust our internal ratings. 

Asset-swap pricing is commonly applied to credit-default swaps, especially by risk management departments seeking to price the transactions held on credit traders book. A par asset swap typically combines an interest rate swap with the sale of an asset, such as a fixed-rate corporate bond, at par and with no interest accrued. The coupon on the bond is paid in return for LIBOR plus, if necessary, a spread, known as the asset-swap spread. This spread is the price of the asset swap. It is a function of the credit risk of the underlying asset. That makes it suitable as the basis for the price payable on a credit default swap written on that asset. 

Non-interest-beanng securities are also referred to as discounted securities. Unlike regular corporate bonds, which pay periodic interest (i.e., pay a coupon), interest is earned on these bonds by their appreciation in price over time. That is, these securities originally sell for less than their maturity or face value. All other factors being constant, the price approaches the face value as the time to maturity approaches zero. Note that this is not the same thing as a coupon bond that is selling at a discount. 

Most corporate bonds, as well as municipals and Treasury notes and bonds, pay interest on a semiannual basis. To find the interest paid during the year, multiply the par value (face or maturity value) of the bond by the annual coupon rate. This amount is then divided by 2 to determine the amount of interest paid every 6 months. It is important to know that corporate securities use a 180-day coupon period—a commercial year of 360 days or 30 days per month, whereas government securities use an exact year of 365 days (366 days for a leap year). In addition, corporate securities are delivered 5 business days after the sale, whereas government securities are delivered the same day or the day after the sale. Prices for these securities are calculated as of the delivery date. Finally, if a bond is sold between coupon dates, it will have accrued interest since the last coupon date. This accrued interest must be added to the quoted price to determine the actual amount that the investor is required to pay. 

The quoted price of a bond is equal to the present value of the future cash flows to be received minus the accrued interest. Bonds are priced as of the delivery date. Corporate bonds assume a 180-day coupon period, whereas government securities use the exact number of days within the coupon period. Thus, for bonds not selling at a coupon date, a distinction must be made between corporate and government securities. 

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