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Optimal Hedging of Basket Barrier Options with Additive Models and Its Application to Equity Value Separation Problem

Content Provider	Springer Nature Link
Author	Yamada, Yuji
Copyright Year	2017
Abstract	At the heart of optimal hedging with additive models in Yamada (Recent advances in financial engineering: proceedings of the KIER-TMU international workshop on financial engineering, World Scientific, pp 225–245, 2010; Proceedings of the 2011 American control conference, pp 3856–3861, 2011; Asia-Pac Financ Mark 19(2):149–179, 2012) is to replicate the payoff of European basket options using separate options as close as possible. In this paper, we extend their technique for the case of path-dependent barrier options, where the mean square error of the payoffs between the basket barrier option and the sum of options on the individual assets is minimized over any smooth payoff functions. To this end, we propose to represent the underlying assets using the Brownian bride decomposition and show that computations involving conditional expectations of basket barrier options boil down to those of unconditional expectations. This procedure enables us to provide an algorithm to compute the necessary and sufficient condition for the optimal hedging problem based on the Monte Carlo method. Then, we consider to apply our methodology to the Black–Cox type first passage time structural model, where a defaultable company possesses/runs multiple assets/projects and the default may occur the first time the asset value hits a certain lower threshold before the maturity. We formulate the equity value separation problem using additive models, in which individual equity values are introduced so that their sum approximates the total equity value as close as possible. It is also shown that any portion of total equity value may be assigned as an initial value of each individual equity when using the optimal smooth functions. Finally, we examine the contributions of individual equity values to default or survival by applying a certain normalization for conditional expectations via numerical experiments to illustrate our proposed methodology.
Starting Page	1
Ending Page	18
Page Count	18
File Format	PDF
ISSN	13872834
Journal	Asia-Pacific Financial Markets
Volume Number	24
Issue Number	1
e-ISSN	15736946
Language	English
Publisher	Springer Japan
Publisher Date	2017-01-09
Publisher Place	Tokyo
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Basket barrier options Optimal hedging Additive models Smooth functions First passage time structural models Finance Macroeconomics/Monetary Economics//Financial Economics International Economics Econometrics Economic Theory/Quantitative Economics/Mathematical Methods
Content Type	Text
Resource Type	Article
Subject	Finance

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