Abstract-In this paper, a Hidden Markov Model is employed to fit global, U.S. and European annual corporate default counts. The Expectation-Maximization algorithm is applied to calibrate all parameters while the standard errors of the estimated parameters are conducted by Monte Carlo method. Parametric bootstraps are used to compute the nonlinear forecasts. The empirical results show that the Hidden Markov model is useful in distinguishing the periods of expansion from the periods of recession (relative to the points identified by the NBER). Moreover, it obtains relatively satisfactory forecasts especially in capturing the state switching while incorporating more original observations.
IndexTerms-Corporate default counts, expectation-maximization algorithm, hidden Markov model, parametric bootstrap.
I. INTRODUCTIONThe issue regarding estimating potential risk levels and forecasting default events of financial assets has increasingly became the interest of many financial, economic, and mathematical researchers in contemporary society. Previously, due to the achievement of Moody [1], the Binomial Expansion Technique (BET) was created to estimate the expected loss of collateralized bond and loan obligations (CBOs and CLOs). However, it is ideal that there exists a pure binomial distribution with independent defaults. With the introduction of diversity score which is used to distinguish a smaller portfolio of independent and homogenous financial assets, it is easier to assume that all these financial assets (bonds and loans) have the same default probability and default independently, resulting in the binominal distribution regarding the quantity of observed default events in single time stage. More importantly, as mentioned by Düllmann [2], some shortages of BET method can be optimized to some extent by the model created by Davis and Lo [3]. In particular, it was related to infectious defaults which increase the default risk of other financial assets. There are two types of risk (normal risk and enhanced risk, respectively), and the latter risk level is enhanced by multiplying infectious factor k. In this case, the similar approach named Hidden Markov Model will be used to detect risk periods in the economy, and related parameters are estimated by Expectation-Maximization algorithm (EM algorithm). More importantly, what this paper pays more attention to concerns corporate default counts forecast, which is different from emphasizing on estimation process and detection of expansion and recession periods in previous researches. The forecast process is achieved by the parametric bootstrap approach according to Tsay [4], which is used to perform the nonlinear forecasts.The content of this paper is divided into six aspects. Detailed methods or approaches utilized in this article will be included and explained in Section II and the simulation part Section III is to test the effectiveness of parameter estimation. Then imperial analysis in Section IV incorporates some small related aspects, data introduction, for example. S...
