Bootstrapping is a resampling method that has a wide variety of applications. It can be used to simulate the trajectories of sample paths, to determine if an estimator generated from real-world data has an approximate distribution, or to derive standard errors of a complicated estimator.
We obtain credit default swap index data developed by Datastream, a Thomson Financial product, covering the corporate debt of the automobile and automobile parts sector from January 1, 2004 through July 21, 2008. The credit default swap index used in this analysis should be interpreted as the average number of basis points per year required to insure against default on the debt obligations of companies in the U.S. domestic automobile sector (the average is taken at each point in time with respect to the relative weights of the then-current market value of the underlying debt issues). Using a bootstrapping technique, we simulate future trajectories of this particular credit default swap index.
We assume that the log-returns of the credit default swap (CDS) index are independent and identically distributed. After computing the set of log-returns in the automobile and automobile parts CDS index for the period from January 1, 2004 through July 21, 2008, we resample from the empirical distribution to obtain projected log-returns for the index for a length of time specified by the user. We then reconstitute the future projected index using the latest observed value of the index.
A credit default swap (CDS) is a bilateral contract, typically possessing counter-party risk, under which two parties agree to isolate and trade the credit risk of at least one third-party reference entity. The buyer of the swap receives credit protection and pays a premium periodically to the seller of the swap. If a "credit event'' occurs (typically failure to make a coupon or principal payment, but also possibly failing to maintain certain financial ratios), then the seller of the swap is obligated to purchase the bond from the swap buyer at par value. Credit default swaps can also be settled in the cash market; after a credit event occurs, the seller can simply pay the buyer the difference between the new (typically much lower) price of the bond and the par value of the bond.
Datastream, a popular data service owned by Thomson Financial, produces a family of credit default swap indices. Some of these indices are organized by U.S. economic sectors. Moreover, they are effectively market-weighted (by the market weights of the underlying bond instruments) averages of relatively liquid credit default swaps. The sector-based credit default swap indices produced by Datastream include automobile and related parts, banks, basic resources, chemicals, construction and materials, financial services, food and beverages, health care, industrial goods and services, insurance, media, oil and gas, personal and household goods, real estate, retail, technology, telecommunications, travel and leisure, and utilities. Various credit default swap indices for various economic sectors are available for the United States, Japan, the United Kingdom, and Europe. We study the automobile and related parts CDS index.
We note that the technique of bootstrapping future trajectories of economic variables (like asset prices or credit default swap data) is not immune to criticism. It is potentially problematic to rely on the assumption that some aspects of the time series (in our case, the log-returns) are independent and identically distributed. In particular, one can argue that in the current credit crisis, credit default swap premiums are extraordinarily high, and that they will "revert to the mean" in the near-term. Most of the projections we make result in a credit default swap index that remains rather high for the foreseeable future.