| We examine methods to extract various types of information from derivative prices by means of continuous time models and modern estimation and filtering methods. The first essay introduces the approach allowing the joint estimation of the objective and risk-neutral measures based on the time series of assets returns and options prices in the stochastic volatility model framework. The second essay develops a model, which allows for simultaneous consideration of multiple assets and their derivatives. This model, when combined with the filtering techniques, allows for unbiased estimation of the stochastic discount factor without any initial assumptions about the utility function. The third essay extends the approach by suggesting a new class of jump diffusion models, which allows for analytical option pricing. The various estimation strategies are discussed. |
