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Optimal Hedging with Additive Models

In: Recent Advances In Financial Engineering 2010

Author

Listed:
  • Yuji Yamada

    (Graduate School of Business Sciences, University of Tsukuba, 3-29-1 Otsuka, Bunkyo-ku, Tokyo 112-0012, Japan)

Abstract

In this paper, we consider optimal hedges for a class of derivative securities whose underlyings are untraded using the additive sum of smooth functions of traded assets that minimizes their mean square errors. At first, we show that the general problem is reduced to a system of linear operator equations, and derive a methodology to obtain the optimal smooth functions efficiently based on suitable discretization. Then, we extend the idea to basket options consisting of the weighted sum of many stocks, where smooth payoff functions of individual assets are computed to approximate the terminal payoff of basket option as close as possible in the minimum mean square sense. Numerical experiments are also provided to illustrate our proposed methodology.

Suggested Citation

  • Yuji Yamada, 2011. "Optimal Hedging with Additive Models," World Scientific Book Chapters, in: Masaaki Kijima & Chiaki Hara & Yukio Muromachi & Hidetaka Nakaoka & Katsumasa Nishide (ed.), Recent Advances In Financial Engineering 2010, chapter 11, pages 225-245, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789814366038_0011
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