| Summary: | 碩士 === 國立臺灣大學 === 國際企業學研究所 === 93 === In Kifer (2000), a new derivative security called game option was introduced. Game option, also called Israeli option, is a contract which enables both its holder (buyer) and writer (seller) to stop it at any time before expiration. That is, its buyer can exercise the right to buy (for a call) or to sell (for a put) a specified underlying asset at a predetermined price, and its seller can cancel the contract by paying the buyer the early exercise payoff plus an amount of penalty. Although some literatures probed into the valuation model of this new derivative, efficient numerical methods have not been developed yet, and both its free boundary problem and the corresponding variational inequalities have not been constructed. Throughout this thesis, we only consider the most general case of game-type contingent claims for its valuation. First we propose the rules of penalty format, choose a more practical one, and apply the familiar binomial tree method. Then we construct its free boundary problem, formulate the corresponding variational inequalities, and use finite-difference method to solve it. Finally, we compare the above results and bring up some discussions.
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