A general option pricing framework for affine fractionally integrated models

IF 3.6 2区 经济学 Q1 BUSINESS, FINANCE
Maciej Augustyniak , Alexandru Badescu , Jean-François Bégin , Sarath Kumar Jayaraman
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引用次数: 0

Abstract

This article studies the impact of fractional integration on volatility modelling and option pricing. We propose a general discrete-time pricing framework based on affine multi-component volatility models that admit ARCH() representations. This not only nests a large variety of option pricing models from the literature, but also allows for the introduction of novel covariance-stationary long-memory affine GARCH pricing models. Using an infinite sum characterization of the log-asset price’s cumulant generating function, we derive semi-explicit expressions for the valuation of European-style derivatives under a general variance-dependent stochastic discount factor. Moreover, we carry out an extensive empirical analysis using returns and S&P 500 options over the period 1996–2019. Overall, we find that once the informational content from options is incorporated into the parameter estimation process, the inclusion of fractionally integrated dynamics in volatility is beneficial for improving the out-of-sample option pricing performance. The largest improvements in the implied volatility root-mean-square errors occur for options with maturities longer than one year, reaching 28% and 18% when compared to standard one- and two-component short-memory models, respectively.
仿射分数积分模型的一般期权定价框架
本文研究了分数积分对波动率建模和期权定价的影响。我们提出了一个基于仿射多分量波动率模型的通用离散时间定价框架,该模型允许ARCH(∞)表示。这不仅包含了文献中大量的期权定价模型,而且还允许引入新的协方差平稳长记忆仿射GARCH定价模型。利用对数资产价格累积生成函数的无限和特征,我们推导了一般方差相关随机贴现因子下欧式衍生品估值的半显式表达式。此外,我们使用1996-2019年期间的回报和标准普尔500期权进行了广泛的实证分析。总的来说,我们发现,一旦将期权的信息内容纳入参数估计过程,在波动率中包含分数积分动态有利于改善样本外期权定价性能。隐含波动率均方根误差的最大改善发生在期限超过一年的期权上,与标准的单组分和双组分短记忆模型相比,分别达到28%和18%。
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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来源期刊
CiteScore
6.40
自引率
5.40%
发文量
262
期刊介绍: The Journal of Banking and Finance (JBF) publishes theoretical and empirical research papers spanning all the major research fields in finance and banking. The aim of the Journal of Banking and Finance is to provide an outlet for the increasing flow of scholarly research concerning financial institutions and the money and capital markets within which they function. The Journal''s emphasis is on theoretical developments and their implementation, empirical, applied, and policy-oriented research in banking and other domestic and international financial institutions and markets. The Journal''s purpose is to improve communications between, and within, the academic and other research communities and policymakers and operational decision makers at financial institutions - private and public, national and international, and their regulators. The Journal is one of the largest Finance journals, with approximately 1500 new submissions per year, mainly in the following areas: Asset Management; Asset Pricing; Banking (Efficiency, Regulation, Risk Management, Solvency); Behavioural Finance; Capital Structure; Corporate Finance; Corporate Governance; Derivative Pricing and Hedging; Distribution Forecasting with Financial Applications; Entrepreneurial Finance; Empirical Finance; Financial Economics; Financial Markets (Alternative, Bonds, Currency, Commodity, Derivatives, Equity, Energy, Real Estate); FinTech; Fund Management; General Equilibrium Models; High-Frequency Trading; Intermediation; International Finance; Hedge Funds; Investments; Liquidity; Market Efficiency; Market Microstructure; Mergers and Acquisitions; Networks; Performance Analysis; Political Risk; Portfolio Optimization; Regulation of Financial Markets and Institutions; Risk Management and Analysis; Systemic Risk; Term Structure Models; Venture Capital.
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