Efficient pricing of path-dependent interest rate derivatives

IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Allan Jonathan da Silva, Jack Baczynski, José V. M. Vicente
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引用次数: 0

Abstract

Interest rate derivative pricing is a critical aspect of fixed-income markets, where efficient methods are essential. This study introduces a novel approach to pricing path-dependent interest rate derivatives within a broad class of affine jumps. The study's particular setting is the Fourier-cosine series (COS) method adaptation, which offers an accurate and computationally efficient method for pricing interest rate derivatives. The Fourier-cosine series approach can be used to compute probability density functions and option pricing with a linear computing complexity and exponential convergence rate. The lack of a quick and precise pricing technique for Asian interest rate options in diverse fixed-income market scenarios is a research gap that is being addressed. This approach closes this gap by providing quasi-closed and closed-form equations for a range of density and characteristic functions, resulting in precise pricing. The results demonstrate the versatility of the COS method in interest rate markets. Similar to what has been previously reported for stock options, the numerical findings demonstrate the extreme precision and computing speed of the pricing and hedging estimations provided here. This method is an innovative approach to interest rate derivative pricing, offering researchers and practitioners a powerful tool for efficiently calculating prices and calibrating options across strikes and maturities.

路径依赖利率衍生品的有效定价
利率衍生品定价是固定收益市场的一个重要方面,高效的定价方法至关重要。本研究介绍了一种新方法,用于在仿射跃迁的大类中对路径依赖利率衍生品进行定价。该研究的特定环境是傅立叶-余弦数列(COS)方法适应性,它为利率衍生品定价提供了一种精确且计算效率高的方法。傅立叶-余弦数列方法可用于计算概率密度函数和期权定价,计算复杂度为线性,收敛速度为指数。在各种固定收入市场情况下,亚洲利率期权缺乏快速精确的定价技术,这是一个正在解决的研究空白。这种方法为一系列密度和特征函数提供了准封闭和封闭式方程,从而实现了精确定价,填补了这一空白。研究结果证明了 COS 方法在利率市场中的多功能性。与之前关于股票期权的报告类似,数值结果表明本文提供的定价和对冲估算极其精确,计算速度极快。该方法是利率衍生品定价的一种创新方法,为研究人员和从业人员提供了一种有效计算价格和校准不同行权价和期限期权的强大工具。
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
2.70
自引率
0.00%
发文量
67
审稿时长
>12 weeks
期刊介绍: ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process. The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.
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