This paper describes a GAUSS program of a Markov-chain sampling algorithm for GARCH models proposed by Nakatsuma (1998). This algorithm allows us to generate Monte Carlo samples of parameters in a GARCH model from their joint posterior distribution. The samples obtained by this algorithm are...

This paper describes a GAUSS program of a Markov-chain sampling algorithm for GARCH models proposed by Nakatsuma (1998). This algorithm allows us to generate Monte Carlo samples of parameters in a GARCH model from their joint posterior distribution. The samples obtained by this algorithm are...

There exist several estimators for valuing the Asian option on the arithmetic mean. Among all variance reduction estimators, the one with the control variate derived from the geometric mean has been shown by Boyle et al. (1997) to perform best so far. In this paper, a new improved control...

This paper describes a GAUSS program of a Markov-chain sampling algorithm for GARCH models proposed by Nakatsuma (1998). This algorithm allows us to generate Monte Carlo samples of parameters in a GARCH model from their joint posterior distribution. The samples obtained by this algorithm are...

Three Bayesian methods (Markov chain Monte Carlo, Laplace approximation and quadrature formula) are developed to estimate the parameters of the ARMA-GARCH model. The ARMA-GARCH model is applied to weekly foreign exchange rate data of five major currencies, and their stochastic volatilities are...