标题： 波动率聚集对通过凸风险度量的期权无差异定价的影响 显示英文标题

标题： Effect of Volatility Clustering on Indifference Pricing of Options by Convex Risk Measures

摘要： 在本文中，我们研究了波动率聚集对Sircar和Sturm在其论文中描述的期权风险无差异价格的影响(Sircar, R., & Sturm, S. (2012). 从微笑渐近到市场风险度量. 数学金融. 在线提前出版. doi:10.1111/mafi.12015). 他们在文章中通过由倒向随机微分方程给出的动态凸风险度量得到无差异价格. 波动率聚集通过一个快速均值回归的波动率在一个股票价格的随机波动率模型中进行建模. 本文得到了当均值回归时间趋近于零时期权的无差异价格及其相应隐含波动率的渐近行为. 还得到了渐近期权价格和隐含波动率的修正项. 显示英文摘要

摘要： In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finance. Advance online publication. doi:10.1111/mafi.12015). The indifference price in their article is obtained by using dynamic convex risk measures given by backward stochastic differential equations. Volatility clustering is modelled by a fast mean-reverting volatility in a stochastic volatility model for stock price. Asymptotics of the indifference price of options and their corresponding implied volatility are obtained in this article, as the mean-reversion time approaches zero. Correction terms to the asymptotic option price and implied volatility are also obtained.