Seminar
Department of Systems Engineering and Engineering Management
The Chinese University of Hong Kong
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Title |
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Excursion and Occupation Time of a Diffusion Process in Option Pricing |
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Speaker |
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Dr. Kwai-Sun Leung |
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Risk Management Institute |
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National University of Singapore |
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Date |
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January 2nd, 2008 (Wednesday) |
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Time |
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2:00 p.m.-3:00 p.m. |
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Venue |
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Room 513 |
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William M.W. Mong Engineering Building |
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(Engineering Building Complex Phase 2) |
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CUHK |
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Abstract:
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In general, the excursion and occupation time of a stochastic process measure the amount of time that the process staying on or below (or above) a given level. The difference of them is that the timer for measuring the excursion time will reset when the process hits the barrier, while the timer will not reset in the case of occupation time. Recently, they have received much attention in option design and credit risk modeling.
In this talk, the notion of occupation time and excursion time are used to specify the repricing criteria of the employee stock option. The analytic representations of the price function of the options under these two different repricing criteria are derived. Numerically, the forward shooting grid technique in the lattice tree algorithm is enhanced to handle the path dependent, early exercise and multiple repricing features of the option.
On the other hand, the Feynman-Kac formula is applied to derive the density function of occupation time and the joint density function of occupation time and terminal asset value under the constant elasticity of variance (CEV) process. The derived distribution functions are then used to derive the price formulas of the alpha-quantile options. The fixed-floating symmetry relation for alpha-quantile option is also derived when the underlying asset price process follows the Geometric Brownian motion.
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Biography:
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Dr. Kwai-Sun Leung is a Research Fellow of the Risk Management Institute, National University of Singapore. He received his Ph.D. in Mathematics from Hong Kong University of Science and Technology. His research interests are in the area of exotic option pricing and credit risk modeling.
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