Ebook Realized Jumps on Financial Markets and Predicting Credit Spreads
The relatively large credit spreads on high grade investment bonds has long been an anomaly in financial economics. Historically, firms that issue such bonds appear to entail very little default risk yet their credit spreads are sizable and positive (Amato and Remolona, 2003). A natural explanation is that these firms are exposed to large sudden and unforeseen movements in the financial markets. In other words, the spread accounts for exposure to market jump risk. Jump risk has been proposed before as a possible source of the credit premium puzzle (Zhou, 2001; Huang and Huang, 2003), but the empirical validation in literature has met with mixed and inconclusive results (Collin-Dufresne, Goldstein, and Martin, 2001; Collin-Dufresne, Goldstein, and Helwege, 2003; Cremers, Driessen, Maenhout, and Weinbaum, 2005, 2004). In this paper, we develop a jump risk measure based on identified realized jumps (as opposed to latent or implied jumps) as an explanatory variable for high investment grade credit spread indices.
The continuous-time jump-diffusion modeling of asset return process has a long history in finance, dating back to at least Merton (1976). However, the empirical estimation of the jump-diffusion processes has always been a challenge to econometricians. In particular, the identification of actual jumps is not readily available from the time-series data of underlying asset returns. Most of the econometric work relies on complicated numerical methods, or numerically intensive simulation-based procedures, and/or joint identification schemes from both the underlying asset and the derivative prices (see, e.g., Bates, 2000; Andersen, Benzoni, and Lund, 2002; Pan, 2002; Chernov, Gallant, Ghysels, and Tauchen, 2003; Eraker, Johannes, and Polson, 2003, among others).
This paper takes a different and direct approach to identify the realized jumps based on the seminal work by Barndorff-Nielsen and Shephard (2004b, 2006). Recent literature suggests that the realized variance measure from high frequency data provides an accurate measure of the true variance of the underlying continuous-time process (Andersen, Boller-slev, Diebold, and Labys, 2003b; Barndorff-Nielsen and Shephard, 2004a; Meddahi, 2002). Within the realized variance framework, the continuous and jump part contributions can be separated by comparing the difference between realized variance and bi-power variation (see, Barndorff-Nielsen and Shephard, 2004b; Andersen, Bollerslev, and Diebold, 2004; Huang and Tauchen, 2005). Under the reasonable presumption that jumps on financial markets are usually rare and large, we assume that there is at most one jump per day and that the jump dominates the daily return when it occurs. This allows us to filter out the realized jumps, and further to directly estimate the jump distributions (intensity, mean, and variance). Such an estimation strategy based on identified realized jumps stands in contrast with existing literature that generate noisy parameter estimates based on daily returns.
A?t-Sahalia (2004) examines how to estimate the Brownian motion component by maximum likelihood, while treating the Poisson or Lévy jump component as a nuisance or noise. Our approach is exactly the opposite we estimate the jump component directly and then use the results for further economic analysis. The advantages of this approach include that we do not require the specification and estimation of the underlying drift and diffusion functions and that the jump process can be flexible. Such a jump detection and estimation strategy could be invalid for certain highly active Lévy process with infinite small jumps in a finite time period (Bertoin, 1996; Barndorff-Nielsen and Shephard, 2001; Carr and Wu, 2004). The approach here is more applicable to the compound Poisson jump process, where rare and potentially large jumps in financial markets are presumably the responses to significant economic news arrivals (Merton, 1976).
In Monte Carlo work, we examine two main settings where the jump contribution to total variance is 10% and 80%. In these situations, our realized jump identification approach performs well, in that the parameter estimates are accurate and converge as the sample size increases (long-span asymptotics). One important caveat is that these convergence results depend on choosing appropriately the level of the jump detection test. The significance level needs to be set rather loosely at 0.99 when jump contribution to total variance is low (10%), but set rather tightly at 0.999 when the jump contribution is high (80%). Note that a smaller jump contribution like 10% seems to be the main empirical finding in the literature (see, Andersen, Bollerslev, and Diebold, 2004; Huang and Tauchen, 2005, e.g.).
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