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随机波动率大规模组合中的快速均值回复与损失估计

文章 arXiv papers · 作者: Ben Hambly et al.
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总结

本文研究一个大规模资产组合的损失，该组合中的资产价格遵循随机波动率模型，并在触及下方障碍时违约。一个随机偏微分方程表示组合极限，系统性布朗运动将资产价格与波动率联系起来。研究关注的是损失如何随解的总质量变化。

分析在关于波动率的两种假设下考察快速均值回复。当波动率收敛到极限分布时，系统弱收敛；当只有均值回复速率提高时，则得到更强形式的收敛。这些结果支持在快速均值回复情形下，用更简单的常波动率模型近似损失分布。描述给出了理论收敛结论，但没有数值示例、校准指导，也没有证据说明该近似对特定组合的准确性。

核心观点

  • 该模型通过随机偏微分方程表示大规模可违约资产组合。
  • 系统性布朗运动使资产价格与其波动率产生依赖关系。
  • 损失被建模为系统中剩余总质量的函数。
  • 快速均值回复使得使用常波动率模型进行近似成为可能。
  • 收敛结果取决于波动率在极限状态下的表现。

标签

统计学波动率风险管理
全文
# Fast mean-reversion asymptotics for large portfolios of stochastic volatility models


# Fast mean-reversion asymptotics for large portfolios of stochastic volatility models









We consider an SPDE description of a large portfolio limit model where the underlying asset prices evolve according to certain stochastic volatility models with default upon hitting a lower barrier. The asset prices and their volatilities are correlated via systemic Brownian motions, and the resulting SPDE is defined on the positive half-space with Dirichlet boundary conditions. We study the convergence of the loss from the system, a function of the total mass of a solution to this stochastic initial-boundary value problem under fast mean reversion of the volatility. We consider two cases. In the first case the volatility converges to a limiting distribution and the convergence of the system is in the sense of weak convergence. On the other hand, when only the mean reversion of the volatility goes to infinity we see a stronger form of convergence of the system to its limit. Our results show that in a fast mean-reverting volatility environment we can accurately estimate the distribution of the loss from a large portfolio by using an approximate constant volatility model which is easier to handle.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。