In this paper we present inference methods which are based on an ‘incorrect’ criterion, in the sense that the optimization of this criterion does not directly provide a consistent estimator of the parameter of interest. Moreover, the argument of the criterion, called the auxiliary parameter, may have a larger dimension than that of the parameter of interest. A second step, based on simulations, provides a consistent and asymptotically normal estimator of the parameter of interest. Various testing procedures are also proposed. The methods described in this paper only require that the model can be simulated, therefore they should be useful for models whose complexity rules out a direct approach. Various fields of applications are suggested (microeconometrics, finance, macroeconometrics).

This paper studies a classical extension of the Black and Scholes model for option pricing, often known as the Hull and White model. Our specification is that the volatility process is assumed not only to be stochastic, but also to have long-memory features and properties. We study here the implications of this continuous-time long-memory model, both for the volatility process itself as well as for the global asset price process. We also compare our model with some discrete time approximations. Then the issue of option pricing is addressed by looking at theoretical formulas and properties of the implicit volatilities as well as statistical inference tractability. Lastly, we provide a few simulation experiments to illustrate our results. Copyright Blackwell Publishers Inc 1998.

No abstract

and Toulouse. We also thank R. Lestringand who performed the numerical illustration given in Section 5. 2 Lyxor Asset Management and CREST.

In other words, while the solvability criterion of Kϕ = r imposes r ∈ Ψ for some γ ≥ 1, we will get a geometric rate of decay of the regularization bias as soon as r ∈ Ψ for some γ > 1. Note that the upper bound β = 2 of the rate of decay is just a matter of normalization of the parameter α of regularization. By (3.19), ϕ − ϕ © cannot go to zero faster than [1 − q (α, λ)] ©

No abstract

No abstract

No abstract