具有随机波动率和随机波动率的指数L'Evy型模型 跳跃强度

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

摘要翻译：
我们考虑了一个写在资产上的欧式期权的估值问题，该资产的动力学由指数L\'Evy-type模型描述。在我们的框架中，波动率和跳跃强度都允许通过共同的驱动因素--一个快变和一个慢变--随时间随机变化。利用Fourier分析，我们导出了任意一个欧式导数的近似价格的显式公式，其收益具有广义Fourier变换；特别是，这包括欧洲看涨和看跌。从理论上，我们的结果将Citet*{fpss}的多尺度随机波动率模型推广到指数L\'evy型模型。从金融角度来看，跳跃和随机波动性的加入使我们能够捕捉隐含波动性的期限结构。为了说明我们的建模框架的灵活性，我们扩展了五个指数L\'evy过程，包括随机波动率和跳跃强度。对于每个扩展模型，我们使用单一的波动率和跳跃强度的快速变化因子，对S&P500隐含波动率表面进行校正。结果表明，与传统的指数L\'evy模型和Citet{fpss}的快速均值回复随机波动率模型相比，扩展的框架对隐含波动率的拟合效果明显优于传统的指数L\'evy模型。
---
英文标题：
《Exponential L\'evy-type models with stochastic volatility and stochastic
  jump-intensity》
---
作者：
Matthew Lorig and Oriol Lozano-Carbass\'e
---
最新提交年份：
2013
---
分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
--
一级分类：Quantitative Finance        数量金融学
二级分类：Computational Finance        计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
--
一级分类：Quantitative Finance        数量金融学
二级分类：General Finance        一般财务
分类描述：Development of general quantitative methodologies with applications in finance
通用定量方法的发展及其在金融中的应用
--

---
英文摘要：
  We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential L\'evy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time through common driving factors -- one fast-varying and one slow-varying. Using Fourier analysis we derive an explicit formula for the approximate price of any European-style derivative whose payoff has a generalized Fourier transform; in particular, this includes European calls and puts. From a theoretical perspective, our results extend the class of multiscale stochastic volatility models of \citet*{fpss} to models of the exponential L\'evy type. From a financial perspective, the inclusion of jumps and stochastic volatility allow us to capture the term-structure of implied volatility. To illustrate the flexibility of our modeling framework we extend five exponential L\'evy processes to include stochastic volatility and jump-intensity. For each of the extended models, using a single fast-varying factor of volatility and jump-intensity, we perform a calibration to the S&P500 implied volatility surface. Our results show decisively that the extended framework provides a significantly better fit to implied volatility than both the traditional exponential L\'evy models and the fast mean-reverting stochastic volatility models of \citet{fpss}.
---
PDF链接：
https://arxiv.org/pdf/1205.2398

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖

关键词：波动率 Quantitative Applications Exponential QUANTITATIV framework 随机 fast 指数 volatility