Closed-form likelihood approximation and 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 as the sampling interval shrinks. This method is used to uncover the realignment probability of the Chinese Yuan. Since February 2002, the market-implied realignment intensity has increased fivefold. The term structure of the forward realignment rate, which completely characterizes future realignment probabilities, is hump-shaped and peaks at mid-2004. The realignment probability responds quickly to economic news releases and government interventions.