We propose a non-linear State Space representation to model ATM implied volatilities and to estimate the unobserved stochastic volatility for the underlying asset. We are able to estimate the average volatility risk premia and we can also address the presence of long memory in the unobserved volatility factor. We then applied our methodology to implied volatilities on currency options. These data arise from Over The Counter (OTC) transactions that account for high liquidity. We found that the likelihood function and all the iterative procedures associated with it converge uniformly in the parameter space at very little computational expense
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