带有跳跃的多变量扩散的欧式利差期权定价的伊托-泰勒扩展法

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Ge Wang, Yu-xuan Lu, Qing Zhou, Wei-lin Xiao
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引用次数: 0

摘要

本文提出了一种在无跳跃和有不同类型跳跃的多变量不可还原扩散条件下,通过扩展过渡密度函数进行价差期权定价的新方法。通过准兰佩蒂变换将初始时的扩散矩阵单元化,并应用小时间伊托-泰勒扩张法,我们推导出了有跳跃的多变量扩散的过渡密度扩张系数和价差期权价格的显式递推公式。值得一提的是,我们还给出了基础资产价格过程包含默顿跳跃和双指数跳跃的价差期权价格的闭式计算公式,与现有文献相比具有创新性。我们还详细介绍了收敛性的理论证明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Itô-Taylor Expansion Method of European Spread Option Pricing for Multivariate Diffusions with Jumps

In this paper, we propose a new method for spread option pricing under the multivariate irreducible diffusions without jumps and with different types of jumps by the expansion of the transition density function. By the quasi-Lamperti transform, which unitizes the diffusion matrix at the initial time, and applying the small-time Itô-Taylor expansion method, we derive explicit recursive formulas for the expansion coefficients of transition densities and spread option prices for multivariate diffusions with jumps in return. It is worth mentioning that we also give the closed-form formula of spread option price whose underlying asset price processes contain a Merton jump and a double exponential jump, which is innovative compared with current literature. The theoretical proof of convergence is presented in detail.

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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
70
审稿时长
3.0 months
期刊介绍: Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.
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