Sub-Replication and Replenishing Premium: Efficient Pricing of Multi-State Lookbacks |
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Authors: | Wong Hoi Ying Kwok Yue Kuen |
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Institution: | (1) Department of Statistics, Chinese University of Hong Kong, Shatin, Hong Kong, China;(2) Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China |
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Abstract: | The direct valuation procedure of performing discounted expectation to obtain the prices of multi-state lookback options may
lead to insurmountable complexity and numerical difficulties. The computation may require numerical differentiation of the
joint distribution function of the extremum values, then followed by numerical integration over a semi-infinite domain. In
this paper, we illustrate the use of an alternative approach that significantly simplifies the calculations of multi-state
lookback option prices. The financial intuition behind the new approach involves the choice of a sub-replicating portfolio
and the adoption of the corresponding replenishing strategy to achieve the subsequent full replication of the derivative.
The replenishing premium is obtained by performing the integration of an appropriate distribution function over the range
of asset price within which under replication occurs. The sub-replication and replenishment procedures may be utilized as
hedging strategies for the lookback options. The pricing and hedging properties of multi-state lookback options are also discussed.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | option pricing multi-state lookback options replication strategy |
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