We derive an explicit closed-form representation of mean-variance hedging strategies for models whose asset price follows an exponential additive process. Our representation is given in terms of Malliavin calculus for L\'evy processes . In addition, we develop an approximation method to compute mean-variance hedging strategies for exponential L\'evy models , and illustrate numerical results .
We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin derivatives . In addition, we illustrate numerical results for exponential L\'evy models .
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derive an explicit closed-form representation of
focus on
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strategies
problem
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Our representation is given
Some representations of mean-variance hedging strategies for jump type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described
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calculus for L\'evy processes
derivatives
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develop an approximation method to compute mean-variance hedging strategies
illustrate numerical results
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, and illustrate numerical results