On a derivative pricing theory with jumps and stochastic volatilities

具有跳跃和随机波动的衍生品定价理论

• 批准号: 24830087
• 负责人: YAMAZAKI Akira
• 金额: $ 1.25万
• 依托单位: Hosei University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Research Activity Start-up
• 财政年份: 2012
• 资助国家: 日本
• 起止时间: 2012-08-31 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-24830087/
• 关键词: デリバティブ; 確率ボラティリティ; ジャンプ; 確率的時間変更; レヴィ過程; 時間変更型レヴィ過程

Firstly, adopting the proportional hazard model, which has been recognized to be statistically meaningful for analyzing and estimating financial event risks such as default risk and prepayment risk, we provided an analytical treatment for the valuation problems. Secondly, we developed an approximate formula based on the Gram-Charlier expansion for pricing average options when the underlying asset price is driven by time-changed Levy processes. The time-changed Levy processes are attractive to use for a driving factor of underlying prices because the processes provide a flexible framework for generating jumps, capturing stochastic volatility as the random time change, and introducing the leverage effect. Thirdly, we proposed a pricing method for discretely monitored path-dependent options under the time-changed Levy processes. The key to the method is to derive a general formula for the multivariate characteristic functions of the intertemporal joint distribution of the processes.

首先，我们采用比例风险模型对估值问题进行了分析处理。比例风险模型被认为对违约风险和提前还款风险等财务事件风险的分析和估计具有统计意义。其次，基于Gram-Charlier展开式，推导了标的资产价格受时变Levy过程驱动时平均期权定价的近似公式。随时间变化的Levy过程对于潜在价格的驱动因素很有吸引力，因为该过程提供了一个灵活的框架来产生跳跃，捕捉随机时间变化时的随机波动，并引入杠杆效应。第三，我们提出了一种时变Levy过程下离散监测路径依赖期权的定价方法。该方法的关键是推导出过程间关节分布的多变量特征函数的一般公式。

项目成果

Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Levy Processes

在时变征费流程下通过离散监控对路径依赖选项进行定价

• 发表时间: 2012
• 作者: Yamanoi;J. & Ma;X;Akira Yamazaki;藤村美穂・下木なつみ・竹内和雄;高橋典史;樋浦郷子;山嵜輝
• 通讯作者: 山嵜輝

法政大学 経営学部 山嵜 輝 研究室

法政大学经营学部山崎照研究室

On Valuation with Stochastic Proportional Hazard Models in Finance

金融中随机比例风险模型的估值

• DOI: 10.1142/s0219024913500179
• 发表时间: 2013
• 期刊: International Journal of Theoretical and Applied Finance
• 影响因子: 0.5
• 作者: Yamanoi;J;下木なつみ・藤村美穂・竹内和雄;A. Yamazaki
• 通讯作者: A. Yamazaki