Mean-variance Hedging Strategies In Discrete
Time And Continuous State Space
Author(s)
O. L. V. Costa, A. C. Maiali & A. de C. Pinto
Abstract
In this paper we consider the mean-variance hedging problem of a continuous state
space financial model with the rebalancing strategies for the hedging portfolio
taken at discrete times. An expression is derived for the optimal self-financing
mean-variance hedging strategy problem, considering any given payoff in an
incomplete market environment. To some extent, the paper extends the work of
ˇCerný [1] to the case in which prices may assume any value within a continuous
state space, a situation that more closely reflects real market conditions. An
expression for the \“fair hedging price” for a derivative with any given payoff is
derived. Closed-form solutions for both the \“fair hedging price” and the optimal
control for the case of a European call option are obtained. Numerical results
indicate that the proposed method is consistently better than the Black and Scholes
approach, often adopted by practitioners.
Keywords: discrete-time mean-variance hedging, options pricing, optimal control.
1 Introduction
The problem of hedging options has systematically been the focus of attention
from both researchers and practitioners alike. The complex nature of most
derivatives has led academics to often simplify the conditions under which
trading occurs, proposing models which, albeit computational and mathematically
treatable, do not capture all of the peculiarities of these instruments. When
modelling the dynamics of an asset price, its derivatives and the corresponding
hedging process, the choices of state space and time parameter are determined so as
to simplify themodel’s complexity.However,with respect to hedging, the situation
that more closely follows what is observed in real market conditions is the use
Keywords
discrete-time mean-variance hedging, options pricing, optimal control.
Related Book
Other papers in this volume
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