中文版 | English
Title

PARAMETER ESTIMATION OF BLACK-SCHOLES MODEL BY REINFORCEMENT LEARNING

Alternative Title
用强化学习估计 Black-Scholes 模型中的参数
Author
Name pinyin
XU Wen
School number
12032003
Degree
硕士
Discipline
0701 数学
Subject category of dissertation
07 理学
Supervisor
熊捷
Mentor unit
数学系
Publication Years
2022-05-09
Submission date
2022-07-08
University
南方科技大学
Place of Publication
深圳
Abstract

In the process of pricing options with the Black-Scholes formula, it is necessary to know the volatility of the underlying asset. By studying the method of estimating the parameters in the Black-Scholes model, we can provide a better volatility estimation when we apply the Black-Scholes option pricing formula.

During the research process, we have established a reinforcement learning model, and after theoretical analysis, we give the setting form of rewards and propose to use the  TD(0)  algorithm to estimate the volatility and the expected return. The algorithm's convergence and the effectiveness of the reinforcement learning method are demonstrated.


In the case study, we give some known Black-Scholes models and sample their  trajectories as research data. Then the  TD(0) algorithm is used to estimate the expected return and the  volatility. The data shows that after setting the appropriate reward function and discount factor, the reinforcement learning method can effectively estimate the volatility and expected return.

We also use the maximum likelihood estimation method to estimate    the volatility and the expected return.  By analyzing the estimation characteristics of these two methods and comparing their estimation results, we find that for the  Black-Scholes model, our method is more advantageous to estimate  the expected return.

Keywords
Other Keyword
Language
English
Training classes
独立培养
Enrollment Year
2020
Year of Degree Awarded
2022-06
References List

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Academic Degree Assessment Sub committee
数学系
Domestic book classification number
F830.91
Data Source
人工提交
Document TypeThesis
Identifierhttp://kc.sustech.edu.cn/handle/2SGJ60CL/353159
DepartmentDepartment of Mathematics
Recommended Citation
GB/T 7714
Xu W. PARAMETER ESTIMATION OF BLACK-SCHOLES MODEL BY REINFORCEMENT LEARNING[D]. 深圳. 南方科技大学,2022.
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