跳跃聚类存在下的期权套期保值

IF 0.8 4区经济学 Q4 BUSINESS, FINANCE

Journal of Computational Finance Pub Date : 2018-11-26 DOI:10.21314/JCF.2018.354

Donatien Hainaut, Franck Moraux

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引用次数: 18

摘要

本文分析了存在跳跃聚类的股票期权套期保值策略的有效性。在所提出的模型中，资产由跳跃-扩散过程支配，其中跳跃的到达与过去冲击的幅度相关。这一特性为初始跳跃扩散增加了反馈效应和时间异质性。在介绍了该过程的主要性质后，提出了一种期权定价的数值方法。接下来，我们制定了四种对冲政策，使最终财富的方差最小化。这些策略基于期权价格的一阶和二阶近似值。套期工具是标的资产或另一种选择。这些对冲的表现是通过看跌期权和看涨期权的模拟来衡量的，模型符合标准&；穷人500。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hedging of Options in the Presence of Jump Clustering

This paper analyzes the efficiency of hedging strategies for stock options in the presence of jump clustering. In the proposed model, the asset is ruled by a jump-diffusion process, wherein the arrival of jumps is correlated to the amplitude of past shocks. This feature adds feedback effects and time heterogeneity to the initial jump diffusion. After a presentation of the main properties of the process, a numerical method for options pricing is proposed. Next, we develop four hedging policies, minimizing the variance of the final wealth. These strategies are based on first- and second-order approximations of option prices. The hedging instrument is either the underlying asset or another option. The performance of these hedges is measured by simulations for put and call options, with a model fitted to the Standard & Poor’s 500.

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来源期刊

Journal of Computational Finance BUSINESS, FINANCE-

CiteScore

0.90

自引率

0.00%

发文量

期刊介绍： The Journal of Computational Finance is an international peer-reviewed journal dedicated to advancing knowledge in the area of financial mathematics. The journal is focused on the measurement, management and analysis of financial risk, and provides detailed insight into numerical and computational techniques in the pricing, hedging and risk management of financial instruments. The journal welcomes papers dealing with innovative computational techniques in the following areas: Numerical solutions of pricing equations: finite differences, finite elements, and spectral techniques in one and multiple dimensions. Simulation approaches in pricing and risk management: advances in Monte Carlo and quasi-Monte Carlo methodologies; new strategies for market factors simulation. Optimization techniques in hedging and risk management. Fundamental numerical analysis relevant to finance: effect of boundary treatments on accuracy; new discretization of time-series analysis. Developments in free-boundary problems in finance: alternative ways and numerical implications in American option pricing.