Variance-optimal hedging for processes with stationary independent increments
We determine the variance-optimal hedge when the logarithm of the underlying price follows a process with stationary independent increments in discrete or continuous time. Although the general solution to this problem is known as backward recursion or backward stochastic differential equation, we show that for this class of processes the optimal endowment and strategy can be expressed more explicitly. The corresponding formulas involve the moment, respectively, cumulant generating function of the underlying process and a Laplace- or Fourier-type representation of the contingent claim. An example illustrates that our formulas are fast and easy to evaluate numerically.
|Date of creation:||Jul 2006|
|Date of revision:|
|Publication status:||Published in Annals of Applied Probability 2006, Vol. 16, No. 2, 853-885|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Merton, Robert C., 1975.
"Option pricing when underlying stock returns are discontinuous,"
787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
- Hua He and Neil D. Pearson., 1989.
"Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Infinite Dimensional Case,"
Research Program in Finance Working Papers
RPF-191, University of California at Berkeley.
- Hua He & Neil D. Pearson, 1991. "Consumption and Portfolio Policies With Incomplete Markets and Short-Sale Constraints: the Finite-Dimensional Case," Mathematical Finance, Wiley Blackwell, vol. 1(3), pages 1-10.
- He, Hua & Pearson, Neil D., 1991. "Consumption and portfolio policies with incomplete markets and short-sale constraints: The infinite dimensional case," Journal of Economic Theory, Elsevier, vol. 54(2), pages 259-304, August.
- Hua He and Neil D. Pearson., 1989. "Consumption and Portfolio Policies with Incomplete Markets and Short-Sale Constraints: The Finite Dimensional Case," Research Program in Finance Working Papers RPF-189, University of California at Berkeley.
- Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
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