Extended Black and Scholes model under bankruptcy risk

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:482

Article

Hsu, Yu-Sheng¹  Wu, Cheng-Hsun² 

[1] Natl Cent Univ, Dept Math, Chungli, Taiwan

[2] Soochow Univ, Dept Financial Engn & Actuarial Math, Taipei, Taiwan

关键词: Black and Scholes model;    Geometric Brownian motion;    Option pricing;    Monte Carlo simulation;    Quadratic variation-based estimators;   

DOI  :  10.1016/j.jmaa.2019.123564

来源: Elsevier

【 摘 要 】

In the Black-Scholes system, the underlying asset price model follows a geometric Brownian motion with constant volatility and no occurrence of bankruptcy. These two characteristics contradict real financial observations. In order to agree with the nonconstant feature of the volatility and take bankruptcy risk into consideration, we modify the Black and Scholes model and propose a new model based on the efficient market hypothesis. First, we present some probability properties of the bankruptcy risk by our model and demonstrate the statistical inference for the unknown parameters. We also study the European option pricing problem and propose its statistical computation method. In addition, via a real data analysis, we show that our model captures the trend of the stock prices much better than geometric Brownian motion and clarify that the bankruptcy is a crucial factor to be considered in the Black-Scholes system. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free