Valuation of stock loans with jump risk |
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| Institution: | 1. Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR, PR China;2. Department of Economics and Finance, School of Economics and Management, Tongji University, Shanghai, PR China;1. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma Tor Vergata, 00133 Roma, Italy;2. Electrical and Computer Engineering Department, University of California, Santa Barbara, CA 93106-9560, United States;1. UECE - Research Unit on Complexity and Economics, ISEG, University of Lisbon, Miguel Lupi 20, 1248-079 Lisbon, Portugal;2. SOCIUS/CSG - C.I. Sociologia Económica e das Organizações, ISEG, University of Lisbon, Miguel Lupi 20, 1248-079 Lisbon, Portugal;1. Mechanical Engineering, University of Delaware, Newark, DE 19716, United States;2. Linguistics and Cognitive Science, University of Delaware, Newark, DE 19716, United States;3. Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, United States;1. University of Kairouan, Kairouan, Tunisia;2. University of Carthage, La Marsa, Tunisia;3. University of Sfax, Sfax, Tunisia |
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| Abstract: | A stock loan is a special loan with stocks as collateral, which offers the borrowers the right to redeem the stocks on or before the maturity (Xia and Zhou, 2007, Dai and Xu, 2011). We investigate pricing problems of both infinite- and finite-maturity stock loans under a hyper-exponential jump diffusion model. In the infinite-maturity case, we derive closed-form formulas for stock loan prices and deltas by solving the related optimal stopping problem explicitly. Moreover, we obtain a sufficient and necessary condition under which the optimal stopping time is finite with probability one. In the finite-maturity case, we provide analytical approximations to both stock loan prices and deltas by solving an ordinary integro-differential equation as well as a complicated non-linear system. Numerical experiments demonstrate that the approximation methods for both prices and deltas are accurate, fast, and easy to implement. |
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| Keywords: | Stock loans Derivatives pricing Jump diffusion Stopping time |
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