Multivariate fractional Brownian motion and generalizations of SABR model
Multivariate fractional Brownian motion and generalizations of SABR model
复制标题
多元分数布朗运动和 SABR 模型的推广
DOI：
10.2139/ssrn.4188063
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
M. Musiela
中科院分区：
文献类型：
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作者：
M. Musiela
SABR模型是常方差弹性(CEV)模型的推广。它是由Hagan等人介绍和分析的。(2002)。由于隐含波动率的近似公式，它迅速成为计算上限和掉期波动率报价的市场标准，该公式允许对大量上限和掉期进行实时风险管理。后来，它也被用于外汇和股票市场。该推广将随机波动率引入CEV模型。假设波动过程服从零漂移的几何布朗运动，即没有均值回归的鞅过程。这一假设与引入均值回归的其他随机波动率模型明显不同(⁄：133)。本文提出了CEV和SABR的另一种推广。也就是说，用分数布朗运动代替了波动过程中的布朗运动。这种Modi(Cid：133)阳离子导致了一个问题，即如何确定CEV模型的布朗运动和新的波动过程的分数布朗运动之间的依赖结构。我们将选择与模型中随机驱动因素的多变量自相似特性联系起来。
The SABR model is a generalization of the Constant Elasticity of Variance (CEV) model. It was introduced and analyzed by Hagan et al. (2002). Rapidly it has become the market standard for quoting cap and swaption volatilities thanks to the approximate formula for implied volatility which allowed real time risk management of large books of caps and swaptions. Later on it was also used in FX and equity markets. The generalization introduces stochastic volatility to the CEV model. The volatility process is assumed to follow a geometric Brownian motion with zero drift, i.e., a martingale and no mean reversion. This assumption di⁄ers signi(cid:133)cantly from other models of stochastic volatility, where mean reversion is introduced. In this paper another generalization of CEV and also of SABR is proposed. Namely, the Brownian motion de(cid:133)ning the volatility process is replaced with a fractional Brownian motion. Such modi(cid:133)cation leads to the question of how one should de(cid:133)ne the dependence structure between the Brownian motion of the CEV model and the fractional Brownian motion of the new volatility process. We link the choice to multivariate self-similarity property of stochastic drivers in the model.