Closed-Form Likelihood Estimation of Jump-Diffusions with an Application to the Realignment Risk of the Chinese Yuan

This paper provides closed-form likelihood approximations for multivariate jump-diffusion processes widely used in finance. For a fixed order of approximation, the maximum-likelihood estimator (MLE) computed from this approximate likelihood achieves the asymptotic efficiency of the true yet uncomputable MLE estimator as the sampling interval shrinks. This method is then used to uncover the realignment probability of the Chinese Yuan. Since February 2002, the realignment intensity implicit in the financial market has increased fivefold. The term structure of the forward realignment rate, which completely characterizes realignment probabilities in the future, is hump-shaped and peaks at six months from the end of 2003. The realignment probability responds quickly to news releases on the Sino-US trade surplus, state-owned enterprise reform, Chinese government tax revenue and, most importantly, government interventions.