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On the Hoggard–Whalley–Wilmott Equation for the Pricing of Options with Transaction Costs |
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| Authors: | Hitoshi Imai Naoyuki Ishimura Ikumi Mottate Masaaki Nakamura |
| Affiliation: | (1) Department of Informatics and Mathematical Science, Institute of Technology and Science, The University of Tokushima, Tokushima 770-8506, Japan;(2) Department of Mathematics, Graduate School of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan;(3) Graduate School of Commerce and Management, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan;(4) Present address: The Japan Research Institute, Tokyo 102-0082, Japan;(5) Present address: College of Science and Technology, Nihon University, Kanda-Surugadai, Tokyo 101-8308, Japan |
| Abstract: | The Hoggard–Whalley–Wilmott equation is introduced to model portfolios of European type options incorporating transaction costs. The model gives rise to a nonlinear parabolic partial differential equation (PDE), whose nonlinearity reflects the presence of transaction costs. We show analytically the existence of solutions which are not necessarily convex nor concave. Numerical treatments are also given, which are devised to effectively handle an infinite domain and unbounded solutions. |
| Keywords: | Transaction costs Hoggard– Whalley– Wilmott model Nonlinear partial differential equations |
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