On the approximation to the optimal rigion

关于最佳区域的近似

• 批准号: 12630028
• 负责人: TAKAHASHI Hajime
• 金额: $ 1.92万
• 依托单位: Hitotsubashi University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12630028/
• 关键词: Barrier option; Square root boundary; Nonlinear renewal theorem; Forward risk adjusted model; Barrier option; Square root boundary; Nonlinear renewal theorem; Forward risk adjusted model; Martingale法; Jamshidianの方法; 最適停止問題; アメリカン・オプション

We considered new type of barrier type options. Unlike the ordinary barrier options, which have either straight line or constant barrier in terms of the underlying Brownian motion, our barrier is proportional to the square root of the time (Exponential Square root Barrier Knockout Option). Since the fluctuation of Brownian motion is proportional to the square root of the time, our barrier is more natural than the others. We have used the results of Siegmund (1985) and Morimoto (1999) for calculating the necessary probabilities. In addition to the above, we have also considered the discrete time version of the Exponential Square Root Barrier Knockout Options. We have used the asymptotic expantion for the non-linear renewal theorem given by Takahashi-Woodroofe (1981, 1982) for calculating necessary conditional probabilities. The extentons to American type option may be obtained by combining our result with Aitsahilia-Lai (2000), the final result is yet to come though.

我们考虑了新型的屏障类型选项。与普通的屏障选项（在基础布朗运动方面具有直线或恒定屏障）不同，我们的屏障与时间的平方根成正比（指数方形的平方根屏障敲除选项）。由于布朗运动的波动与时间的平方根成正比，因此我们的障碍比其他障碍更自然。我们已经使用了Siegmund（1985）和Morimoto（1999）的结果来计算必要的概率。除上述内容外，我们还考虑了指数方形屏障敲除选项的离散时间版本。我们已经将渐近的指示用于高桥 - 沃德夫（Takahashi-Woodfoode）（1981，1982）给出的非线性更新定理，以计算必要的条件概率。可以通过将我们的结果与Aitsahilia-lai（2000）相结合，可以获得美国类型选择的范围，但最终结果尚未得出。

项目成果

HAJIME TAKAHASMI: "A Note on Interaction between Financial Markets"Asra-Pacific Financial Markets. 7. 155-177 (2000)

HAJIME TAKAHASMI：“关于金融市场之间相互作用的说明”Asra-Pacific 金融市场。

Gaku, Takahashi: "Two Factor Risk Adjusted Measure and Pricing of Derivatives"Proceedings of JAFEE 2001. 281-291 (2001)

Gaku, Takahashi：“双因素风险调整措施和衍生品定价”JAFEE 2001 会议记录。281-291 (2001)

Takahashi, Gaku: "Two factor forward risk adjusted measure and pricing of derivatives"Preadings Jafee 2001 at Gakushuin Univ.. 281-299 (2001)

Takahashi, Gaku：“双因素远期风险调整措施和衍生品定价”Preadings Jafee 2001 at Gakushuin Univ.. 281-299 (2001)

M. Morimoto and H. Takahashi: "On Pricing Exponential Squrare Root Barrier Knockout European Options"Asia-Pacific Financial Markets. 9. 1-21 (2002)

M. Morimoto 和 H. Takahashi：“关于指数平方根障碍淘汰欧洲期权的定价”亚太金融市场。

G. Shin and H. Takahashi: "Two Factor Forward Risk Adjusted Measure and Pricing Derivatives"Proceedings of JAFEE Conference 2001 Winter. 281-291 (2001)

G. Shin 和 H. Takahashi：“双因素远期风险调整措施和定价衍生品”JAFEE 会议 2001 年冬季会议记录。