Estimating structural credit risk models when market prices are contaminated with noise

Abstract

In this paper, sequential estimation on hidden asset value and model parameter estimation is implemented under the Black-Cox model. To capture short-term autocorrelation in the stock market, we assume that market noise follows a mean reverting process. For estimation, Bayesian methods are applied in this paper: the particle filter algorithm for sequential estimation of asset value and the generalized Gibbs and multivariate adapted Metropolis methods for model parameters estimation. The first simulation study shows that sequential hidden asset value estimation using both option price and equity price is more efficient than estimation using equity price alone. The second simulation study shows that, by applying the generalized Gibbs sampling and multivariate adapted Metropolis methods, model parameters can be estimated successfully. In an empirical analysis, the stock market noise for firms with more liquid stock is estimated as having smaller volatility.The mean reverting process assumption is closer to real stock market behavior, which shows short-term dependence. The stock price depends on its previous values, but the shocks to stock prices are all temporary, and stock prices will eventually return to the trend path. Explanations for and empirical testing of the existence of autocorrelation in the stock market are well documented in the studies of Lo and Mackinlay [10,11], Sias and Starks [12], and Chordia and Swaminathan [13]. Following on from the studies of DeBondt and Thaler [14], Poterba [15], and Fama and French [16], who demonstrated the mean reversion property of stock prices, in recent years, there has been increasing evidence supporting the mean reversion hypothesis [17][18][19][20][21].Second, we estimate parameters and unknown asset processes together under the Black-Cox structural model [22]. Previous studies on estimation [6,7] were based on the Merton model, which gives a relatively simple inverse function of equity and asset values. The iterative scheme [23] and the well-known Kealhofer, McQuown and Vasicek (KMV) method (or transformed-data maximum likelihood (ML) method described in the study of Duan [24,25]) are based on the Merton model. However, the study of Jones et al. [26] showed that the predicted bond price for 1977-1981 obtained from the Merton model was over-estimated by 4.52% on average.The Black-Cox model assumes that default can occur at any time prior to the maturity of the bond. It has a default assumption that is more relaxed and closer to the real world, in that under the usual bond contract in practice, a firm needs to pay annual interest to the bond holder, meaning that default can occur at any time before the bond matures. Third, we model the prices of multiple asset classes (debts, equity, and options on equity) in order to gain a better understanding of a firm's capital structure as a whole and also to enhance the precision of the estimation. In the financial market, corporations tend to issue multiple classes of securities to raise their capital. Therefore, the stock marke...

Particle filtering of volatility dynamics for KOSPI200 and its sequential prediction

“…Moreover, the noise term is necessary for model identification. Kwon and Lee (2016) address the market noise and model misspecification error in more detail.…”