泡沫资产建模与定价的随机树

IF 1 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Time Series Analysis Pub Date : 2024-12-05 DOI:10.1111/jtsa.12801

Christian Gourieroux, Joann Jasiak

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引用次数: 0

摘要

我们引入了一种新的严格平稳次鞅过程的随机树表示，用于对商品和加密货币市场的投机泡沫进行建模、预测和定价。将该模型与其他关于泡沫资产建模和随机波动近似的文献中提出的树进行了比较。我们表明，所提出的模型是著名的布兰查德-沃森泡沫的延伸。该模型提供了欧式期权（欧式期权）的（准）封闭式定价公式，并对其进行了推导和说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

A Stochastic Tree for Bubble Asset Modelling and Pricing

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A Stochastic Tree for Bubble Asset Modelling and Pricing

We introduce a new stochastic tree representation of a strictly stationary submartingale process for modelling, forecasting, and pricing speculative bubbles on commodity and cryptocurrency markets. The model is compared to other trees proposed in the literature on bubble asset modelling and stochastic volatility approximation. We show that the proposed model is an extension of the well-known Blanchard-Watson bubble. The model provides (quasi) closed-form pricing formulas for European options, which are derived and illustrated.

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来源期刊

Journal of Time Series Analysis 数学-数学跨学科应用

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： During the last 30 years Time Series Analysis has become one of the most important and widely used branches of Mathematical Statistics. Its fields of application range from neurophysiology to astrophysics and it covers such well-known areas as economic forecasting, study of biological data, control systems, signal processing and communications and vibrations engineering. The Journal of Time Series Analysis started in 1980, has since become the leading journal in its field, publishing papers on both fundamental theory and applications, as well as review papers dealing with recent advances in major areas of the subject and short communications on theoretical developments. The editorial board consists of many of the world''s leading experts in Time Series Analysis.