用于衍生品定价的均值回复随机波动模型的局部波动修正

IF 2.9 3区 经济学 Q1 ECONOMICS
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引用次数: 0

摘要

一般来说,在真实市场中,实证研究结果表明,无论是本地波动率(LV)模型还是随机波 动率(SV)模型,在捕捉给定股票期权隐含波动率的全部动态和几何特征方面都有其局限 性。在本研究中,为了克服 LV 和 SV 模型的缺点,我们提出了一种特殊的混合随机-局部波动率 (SLV∗)模型,在这种模型中,波动率是由标的资产价格的平方对数函数加上快速均值回复 过程的函数给出的。通过利用渐近分析和梅林变换,我们推导出了 SLV∗ 模型下具有平稳和非平稳回报的欧洲衍生品的解析定价公式。我们使用蒙特卡洛模拟法进行了数值实验,以验证定价公式的准确性,结果表明,与其他模型(如赫斯顿模型、随机方差弹性(SEV)模型、混合随机和 CEV 型局部波动率(SVCEV)模型以及多尺度随机波动率(MSV)模型)相比,所提出的新模型更贴近市场隐含波动率的几何形状,尤其是对于短期到期期权而言。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A local volatility correction to mean-reverting stochastic volatility model for pricing derivatives

Generally, in the real market, empirical findings suggest that either local volatility (LV) or stochastic volatility (SV) models have a limit to capture the full dynamics and geometry of the implied volatilities of the given equity options. In this study, to overcome the disadvantage of such LV and SV models, we propose a special type of hybrid stochastic-local volatility (SLV) model in which the volatility is given by the squared logarithmic function of the underlying asset price added to a function of a fast mean-reverting process. By making use of asymptotic analysis and Mellin transform, we derive analytic pricing formulas for European derivatives with both smooth and non-smooth payoffs under the SLV model. We run numerical experiments to verify the accuracy of the pricing formulas using a Monte-Carlo simulation method and to display that the proposed new model fits the geometry of the market implied volatility more closely than other models such as the Heston model, the stochastic elasticity of variance (SEV) model, the hybrid stochastic and CEV type local volatility (SVCEV) model and the multiscale stochastic volatility (MSV) model, especially for short time-to-maturity options.

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来源期刊
CiteScore
6.00
自引率
2.90%
发文量
118
期刊介绍: The Quarterly Review of Economics and Finance (QREF) attracts and publishes high quality manuscripts that cover topics in the areas of economics, financial economics and finance. The subject matter may be theoretical, empirical or policy related. Emphasis is placed on quality, originality, clear arguments, persuasive evidence, intelligent analysis and clear writing. At least one Special Issue is published per year. These issues have guest editors, are devoted to a single theme and the papers have well known authors. In addition we pride ourselves in being able to provide three to four article "Focus" sections in most of our issues.
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