Parameter Learning and Change Detection Using a Particle Filter With Accelerated Adaptation

Indeed, the bulk of the empirical academic literature in finance takes this approach. However, practitioners' use of models, in particular for the pricing and risk management of derivative financial products relative to observed prices for liquidly traded market instruments, typically tends to depart from this ideal. Primacy is accorded to model "calibration" over empirical consistency, i.e., choosing a set of liquidly traded market instruments (which may include liquidly traded derivatives) as "calibration instruments", model parameters are determined so as to match model prices of these instruments as closely as possible to observed market prices at a given point in time. Once these market prices have changed, the model parameters (which were assumed to be constant, or at most time-varying in a known deterministic fashion) are recalibrated, thereby contradicting the model assumptions. "Legalising" these parameter changes by expanding the state space (e.g. via regime-switching or stochastic volatility models) shifts, rather than resolves, the problem: for example in the case of stochastic volatility, volatility becomes a state variable rather than a model parameter, and can evolve stochastically, but the parameters of the stochastic volatility process itself are assumed to be time-invariant.