Abstract
Using observations of an underlying instrument's price series and of derivative prices, we consider the filtering problem of jointly tracking real-world measure parameters and stochastic discount factor parameters. A state-space model of the evolution of the price processes is used, and the filtering is performed through sequential Monte Carlo. Variance gamma and normal inverse Gaussian models of the price process are used as examples. The filter output is used to find diagnostic values such as value-at-risk and expected price change. Both models track these realistically; implementations are presented illustrating the gain in information obtained over standard methods.
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