Optimal Hedging with Additive Models

Yuji Yamada
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Yuji Yamada: Graduate School of Business Sciences, University of Tsukuba, 3-29-1 Otsuka, Bunkyo-ku, Tokyo 112-0012, Japan

Chapter 11 in Recent Advances in Financial Engineering 2010, 2011, pp 225-245 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractIn 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.

Keywords: Operations Research; Financial Engineering; Management; Mathematical Modeling; Credit Risk; Real Options; Optimal Investment; Heterogeneous Beliefs (search for similar items in EconPapers)
Date: 2011
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