On quadratic cost criteria for option hedging

On quadratic cost criteria for option hedging

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Article ID: iaor19941672
Country: United States
Volume: 19
Issue: 1
Start Page Number: 121
End Page Number: 131
Publication Date: Feb 1994
Journal: Mathematics of Operations Research
Authors:
Keywords: programming: dynamic, stochastic processes
Abstract:

Consider an option with maturity time T corresponding to a contingent claim H (in an incomplete market). A fair hedging price for H should take into account an optimal dynamical hedging plan against H. Let Ct be the cumulative cost and t be the set of events of the history up to time t. A plan can be chosen at time t such that (i) E[{CtÅ+1-Ct}2•ℝt], (ii) E[{CT-Ct}2•ℝt], or (iii) E[{CT-C0}2] is minimized. Sufficient conditions on the underlying stochastic process (in discrete time) are provided such that the fair hedging price does not depend on the choice of (i), (ii), or (iii), which fact should increase its acceptability.

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