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This paper extends stochastic conditional duration (SCD) models for financial transaction data to allow for correlation between error processes or innovations of observed duration process and latent log duration process. Novel algorithms of Markov Chain Monte Carlo (MCMC) are developed to fit the resulting SCD models under various distributional assumptions about the innovation of the measurement equation. Unlike the estimation methods commonly used to estimate the SCD models in the literature, we work with the original specification of the model, without subjecting the observation equation to a logarithmic transformation. Results of simulation studies suggest that our proposed models and corresponding estimation methodology perform quite well. We also apply an auxiliary particle filter technique to construct one-step-ahead in-sample and out-of-sample duration forecasts of the fitted models. Applications to the IBM transaction data allows comparison of our models and methods to those existing in the literature.

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In this paper, we propose a novel method of hedging path-dependent options in a discrete-time setup. Assuming that prices are given by the Black–Scholes model, we first describe the residual risk when hedging a path-dependent option using only an European option. Then, for a fixed hedging interval, we find the hedging option that minimizes the shortfall risk, which we define as the expectation of the shortfall weighted by some loss function. We illustrate the method using Asian options, but the methodology is applicable to other path-dependent contacts.