Forecasting Latent Volatility through a Markov Chain Approximation Filter

We propose a new methodology for filtering and forecasting the latent variance in a two‐factor diffusion process with jumps from a continuous‐time perspective. For this purpose we use a continuous‐time Markov chain approximation with a finite state space. Essentially, we extend Markov chain filters to processes of higher dimensions. We assess forecastability of the models under consideration by measuring forecast error of model expected realized variance, trading in variance swap contracts, producing value‐at‐risk estimates as well as examining sign forecastability. We provide empirical evidence using two sources, the S&P 500 index values and its corresponding cumulative risk‐neutral expected variance (namely the VIX index). Joint estimation reveals the market prices of equity and variance risk implicit by the two probability measures. A further simulation study shows that the proposed methodology can filter the variance of virtually any type of diffusion process (coupled with a jump process) with a non‐analytical density function.