CAPÍTULO I EL OBJETO DE TUTELA EN LOS DELITOS RELATIVOS A
III. BASES PARAR LA CONCRECIÓN DEL BIEN JURÍDICO PROTEGIDO EN
6. Paridades y disparidades entre los secretos de empresa y los derechos de
6.1. Características comunes de los secretos de empresa y los derechos de
One obvious component of spread is the expected loss on corporate bond due to default.
We adapt the same bracketing technique as mentioned in Longstaff’s paper for companies with more than one bond available, although we do not eliminate companies that have only one bond in the market.5 The advantage of using bracketing bonds for the same entity is that it provides a better approximation of the credit spread at 5 year horizon, by reducing the idiosyncratic risk that is embedded in individual bonds.
We use the same underlyings as in the selection of reference entities in the CDS spread, certain criteria are performed in order to filter out bond with poor maintenance history or quality:
• Only SEC-registered Euro bonds are included;
• We pick the period between July 1, 2004, and June 30, 2007 as observation period, which means we need complete quotes from both the CDS and bond markets between the observation period, therefore candidate bonds should exist before July 1, 2004, and mature after June 30, 2007.
• where possible, larger issuers are chosen. Issuers with total notional amount of less than 10 million euros are excluded.
• Only bonds with straight fixed-coupon are chosen, floating coupon bonds and zero coupon bonds are excluded.
• Bonds with convertible features such as callable or puttable bonds are excluded.
5we find that companies with only one bond available in the market, their bond tends to
have a strong indication to the CDS spread, whereas for companies with two many bonds available, the indicative effect tends to be diluted, and companies with many bonds tend to have much poorer liquidity than the single bond company.
CHAPTER 5. COX–INGERSOLL–ROSS MODEL 88
In order to select reference entities with bracketing bonds, at least two bonds are included, as the 5-year maturity date for the period between the beginning and end of observation date (July 1, 2004 to June 30, 2007), is within the period between July 1, 2009 to June 30, 2012. We first attempt to find a bond with a maturity shorter than 5 years as the first observation date for the company, which means we need to find a bond that has maturity between July 1, 2007 to June 30, 2009. Also, we need to find bonds with a maturity longer than 5 years of the last observation date for each company, which means we need to find bonds with maturity later than June 30, 2009. Once the bonds defining the lower and upper limit of the bracketing interval are selected, we then select bonds with intermediate maturity dates to provide a roughly equal spaced coverage of the bracketing interval. Some filtering of the bond yield data is necessary, which concerns yields that change dramatically over a short period of time or yields that have more than a month of missing data for any period between the observation dates, which in fact eliminate a large portion of bond data available from Datastream, a few underlying entities are excluded due to the poor quality of their bond data.
5.3.4.2 Credit Spread Derivation from Bond Data To compute the corporate spread the following procedure is used:
1. The bond yields from Datastream are all default prices, hence clean pric- ing, therefore, for each observation, we need to add accrued interest onto the clean price to get the dirty price of the bond.
2. For each corporate bond in the bracketing set, we calculate the theoretical bond price by discounting all the outstanding coupons plus principle back to each observation date using the discount curve of either benchmark curve or swap curve, we then solve for the yield-to-maturity on a riskless bond with the same maturity date and coupon rate.
yield on the corporate bond gives the yield spread for that particular corporate bond over benchmark curve and swap curve.
4. Regress the yield spreads for each individual bonds in the bracketing set on their maturities in order to obtain a five-year-horizon yield spread for the firm. We then use the fitted value of the regression at a five-year horizon as the estimate of the corporate spread for the firm.
5. Check the results of the spread over the benchmark and swap curve with the statics from Datastream and find out that the results are robust.
Fig. 5.1 plots the yield spread over benchmark and yield spread over swap curve, together with credit default swap premium from the market during the sample period. In the model independent approach, the credit default swap premium is used as the estimate of the default component of the corporate spread. It shows a strong trend of corporate bond spread with CDS premium, however, the CDS spread shows a much closer range with bond spread over swap rather than bond spread over benchmark curve. This is why previous studies such as Longstaff et al. (2005)[58] conclude that swap spread provides a much better proxy for default swap, and there is no clear indication of counterparty risk once swap rates are picked as risk-less curve. However, they ignore counterparty risk in the CDS premium, we show later in fig. 5.2 that by taking the difference between the bond spread over benchmark curve and bond spread over swap curve as a counterparty risk premium, and add it onto CDS premium from the market, the newly adjusted CDS premium will not contain counterparty risk and provide a much closer relationship to the bond spread over benchmark curve, which is theoretically the risk-free curve.