| FOREIGN CURRENCY OPTION PRICING WITH PROPORTIONAL TRANSACTION COSTS |
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| 作者姓名： | Li Shujin Li Shenghong |
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| 作者单位： | [1]Department of Mathematics, Zhejiang University, Hangzhou 310027, China. [2]Jiangsu Teachers University of Technology, Changzhou 213001, China. |
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| 基金项目： | Supported by the Natural Science Foundation of Zhejiang Province （Y604137）; the Altitude College Natural Science Foundation of JiangSu Province （KY205017）. |
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| 摘 要： | The purpose of present work is to examine the financial problem of finding the universal reservation prices of a European call option written on exchange rate when there is proportional transaction costs of trading foreign currency in the market. An approach is suggested to compute the reservation bid-ask price of foreign currency call option based on maximizing the investor＇s expected utility. Option prices are determined from the investor＇s basic portfolio selection problem, without the need to solve a more complex optimization problem involving the insertion of the option payoffs into the terminal value function. Option prices are computed numerically in a Markov chain approximation for the case of exponential utility. Numerical results show that the option price bounds are almost independent of the alternative risk aversion parameter, but the bounds of NT region becomes narrower and the range of values of the initial holding for which the fair price lies within the bid-ask spread is shifted to a lower value when the risk aversion parameter increases.
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| 关 键 词： | 交换率 比例事务价值 有效函数 最佳策略 |
| 收稿时间： | 2006-02-28 |
Foreign currency option pricing with proportional transaction costs |
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| Li Shujin Li Shenghong.FOREIGN CURRENCY OPTION PRICING WITH PROPORTIONAL TRANSACTION COSTS[J].Applied Mathematics A Journal of Chinese Universities,2006,21(4):383-396. |
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| Authors: | Shujin Li Shenghong Li |
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| Institution: | Li Shujin Li Shenghong Department of Mathematics,Zhejiang University,Hangzhou 310027,China. Jiangsu Teachers University of Technology,Changzhou 213001,China. |
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| Abstract: | The purpose of present work is to examine the financial problem of finding the universal reservation prices of a European call option written on exchange rate when there is proportional transaction costs of trading foreign currency in the market. An approach is suggested to compute the reservation bid-ask price of foreign currency call option based on maximizing the investor's expected utility. Option prices are determined from the investor's basic portfolio selection problem, without the need to solve a more complex optimization problem involving the insertion of the option payoffs into the terminal value function. Option prices are computed numerically in a Markov chain approximation for the case of exponential utility. Numerical results show that the option price bounds are almost independent of the alternative risk aversion parameter, but the bounds of NT region becomes narrower and the range of values of the initial holding for which the fair price lies within the bid-ask spread is shifted to a lower value when the risk aversion parameter increases. |
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| Keywords: | exchange rate proportional transaction costs utility function optimal strategy |
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