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的资产波动率的重构方法
  • ISSN号：1000-4424
  • 期刊名称：《高校应用数学学报：A辑》
  • 时间：0
  • 分类：O241.4[理学—计算数学;理学—数学]
  • 作者机构：[1]复旦大学数学研究所,上海200433
  • 相关基金：国家自然科学基金（10431030,10271032）
作者： 叶予璋[1], 伊磊[1]
关键词： BLACK-SCHOLES方程, 波动率, Dupire公式, TIKHONOV正则化, 数值微分, 期权标, Black-Scholes equation, volatility, Dupire formula, Tikhonovregulation, numerical differentiation
中文摘要：

在Black-Scholes公式中，波动率σ是一个非常重要的参数．并且在诸如股票、利率、股指期货等标的资产的交易市场中，人们往往希望知道标的资产未来价格的波动率，从而知道该资产的未来风险结构．但一般来说，由于事件还没有发生，人们对σ的未来走向很难预测．但可以运用Black-Scholes的理论框架，从期权市场获取的信息去重构标的资产价格的波动率．论文使用的是基于Tikhonov正则化的数值微分方法，利用Dupire公式去重构标的资产的未来预期波动率．相对于其他方法，该算法更加快速有效，并且能识别标的资产的预期风险突变。

英文摘要：

In Black-Scholes model, a is an important parameter, which is also not freely observable in the market. The volatility of the future prices of the underlying assets which can be stocks, interest, futures and so on, is a wonder. When one knows the volatility, risk structure of those assets is in hand. It turns out that in practice, it is difficult to forecast the future trends of underlying assets directly. Using Black-Scholes equation, this paper recovers the local volatility of underlying assets from information in the option market. In this paper, based on Tikhonov regulation method, numerical differentiation is used to recover the volatility from Dupire formula. Compared with other methods ,this method is faster and more stable. The outstanding advantage of this method is that it can recognize the risk saltation of underlying assets.

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期刊信息
  • 《高校应用数学学报：A辑》
  • 北大核心期刊（2011版）
  • 主管单位:国家教育部
  • 主办单位:浙江大学 中国工业与应用数学学会
  • 主编：林正炎 李大潜
  • 地址：杭州市玉泉浙江大学数学系
  • 邮编：310027
  • 邮箱：amjcu@zjy.edu.cn
  • 电话：0571-87951602
  • 国际标准刊号：ISSN：1000-4424
  • 国内统一刊号：ISSN：33-1110/O
  • 邮发代号:
  • 获奖情况:
  • 国内外数据库收录:
  • 美国数学评论（网络版）,德国数学文摘,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:3669