Abstract
Motivated by the fact that realized measures of volatility are affected by measurement errors, we introduce a new family of discrete-time stochastic volatility models having two measurement equations relating both the observed returns and realized measures to the latent conditional variance. The first contribution of the paper is to provide an analytical filtering and smoothing recursions for the basic version of the model and an effective MCMC algorithm for richer versions featuring heterogeneous structure in both volatility and leverage. The second contribution is to present the first fully analytical option pricing framework for discrete-time stochastic volatility models.
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