Abstract
In nance and economics, the researchers are interested in the regression with time-dependent data that contain variable constraints. Option pricing and portfolio are two important examples of variable constraint. When such a constraint is appended to a classical regression model, new problems arise naturally, including how to build a constraint-dependent model, how to realize its identi ability of the new model, and how to construct an estimation and test. To solve these fundamental problems, in this study we introduce a remodeling method to treat the variable constraint as a quasi instrumental-variable and further to correct the bias and identify the model. A pro le estimation procedure is suggested to estimate the nonparametric function and parameters in the newly de ned model. The consistency and asymptotic normality are obtained. After showing the nite sample property by a simulation study, a real dataset of stock option is analyzed to further illustrate the new methodology.
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