Option pricing under residual risk and imperfect hedging |
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| Authors: | Xiao-Tian Wang Xiang-Qian Liang Ze-Min Zhou |
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| Institution: | 1. Department of Mathematics, South China University of Technology, Guangzhou, 510640, Guangdong, PR China;2. College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao, 266590, Shandong, PR China;3. College of Information, Renmin University of China, 100872, PR China |
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| Abstract: | This paper is concerned in the option pricing in a discrete time incomplete market. We emphasize the interplay between option pricing and residual risk as well as imperfect hedging. It has been shown that the value of a European option satisfies a hyperbolic, rather than parabolic, partial differential equation. The closed-form solution for this hyperbolic equation has been obtained, which will collapse to the Black–Scholes formula as the time scaling converges to zero. |
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| Keywords: | Residual risk Scaling Option pricing Imperfect hedging Asymptotic approach |
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