多维无套利约束的非参数期权定价

doi:10.16381/j.cnki.issn1003-207x.2021.0239

中国管理科学 ›› 2023, Vol. 31 ›› Issue (7): 60-67.doi: 10.16381/j.cnki.issn1003-207x.2021.0239

多维无套利约束的非参数期权定价

李庆¹, 葛翔宇¹, 向秀莉²

1.中南财经政法大学统计与数学学院，湖北武汉430073；2.武汉纺织大学经济学院，湖北武汉430200

收稿日期:2021-02-02 修回日期:2021-05-08 出版日期:2023-07-17 发布日期:2023-07-17
通讯作者: 向秀莉(1984-)，女（汉族），湖北武汉人，武汉纺织大学经济学院，副教授，博士，硕士生导师，研究方向：金融统计，Email：xlxiang@wtu.edu.cn. E-mail:xlxiang@wtu.edu.cn
基金资助:
国家自然科学基金资助项目(71801226, 71974204)；教育部人文社会科学一般项目(21YJC790065)；国家社会科学基金资助项目(22BTJ011)

Nonparametric Option Pricing under Multivariate No-arbitrage Constraints

LI Qing¹, GE Xiang-yu¹, XIANG Xiu-li²

1. School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China;2. School of Economics, Wuhan Textile University, Wuhan 430200, China

Received:2021-02-02 Revised:2021-05-08 Online:2023-07-17 Published:2023-07-17
Contact: 向秀莉 E-mail:xlxiang@wtu.edu.cn

摘要/Abstract

摘要： 基于现有无套利约束的非参数期权定价模型仅考虑单个期限下行权价格的单因素无套利约束的情形，本文将拓展考虑行权期限、标的资产、波动率和无风险利率等多维因素的无套利约束的非参数期权定价模型。为破解多变量约束的非参数回归模型的求解难题，本文首先通过变量变换对多维约束非参数回归模型进行降维，将多维变量变换成单个变量，可同时实现多个期限合约的估计。然后，将带约束的非参数回归模型转化为二次规划优化模型，使用优化工具箱求解。最后，选取上证50ETF期权交易数据对比实证分析的结果表明，考虑多维无套利约束的非参数期权定价模型的定价效果更优。

关键词: 形态约束；多期限组合；多因素约束；局部多项式；二次规划

Abstract: This existing nonparametric option pricing models under no-arbitrage constraints only considered the constraint of strike price along a single maturity, this paper will incorporate all the no-arbitrage constraints, such as maturity, underlying asset price, risk-free rate, and volatility. It’s difficult to estimate the nonparametric model under multivariate no-arbitrage constraints, we will reduce the dimension by variable transformation, and the multivariate will be reduced to one dimension. The number of option strikes contracts is infinite in single maturity, the problem can be solved by indexed multiple time-to-maturities options portfolios with variable transformation. Then, the nonparametric option pricing model under no-arbitrage constraints can be estimated efficiently using a quadratic programming algorithm, which will be computed easily in soft. Finally, we make empirical analysis by SSE 50 ETF options data, and make conclusion that the pricing effect of nonparametric option pricing model under multivariate no-arbitrage constraints is better than Black-Scholes model.

Key words: No-arbitrage Constraints; Multi-term Portfolio; Multivariate Shape Constraints; Local Polynomials Regression; Quadprog Programing

中图分类号:

F832.5
O12

李庆, 葛翔宇, 向秀莉. 多维无套利约束的非参数期权定价[J]. 中国管理科学, 2023, 31(7): 60-67.

LI Qing, GE Xiang-yu, XIANG Xiu-li. Nonparametric Option Pricing under Multivariate No-arbitrage Constraints[J]. Chinese Journal of Management Science, 2023, 31(7): 60-67.

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多维无套利约束的非参数期权定价

Nonparametric Option Pricing under Multivariate No-arbitrage Constraints

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