随机波动率的波动率模型

论文摘要

本文引入了随机波动率的波动率,以对Toy模型进行扩展,从而对实现波动率的衍生品进行定价。文章运用了Toy-Heston模型和Toy-SABR模型,并求得显示解。通过Matlab的实际应用,文章对模型进行了测试对比。实际测试中显现了两个模型的优点和缺点,并指出了模型的潜在用途和提升潜力。

论文目录

• Abstract
• 摘要
• Chapter 1 Introduction
• 1.1 Background
• 1.2 Model specification
• Chapter 2 Model solution
• 2.1 The solution of Toy-Heston model
• 2.1.1 PDE settings
• 2.1.2 Closed form solution
• 2.2 The solution of Toy-SABR model
• 2.2.1 Toy model solution
• 2.2.2 Toy-SABR implied vol of vol
• Chapter 3 Empirical test
• 3.1 Parameters value determination
• 3.2 Model results comparison
• 3.2.1 Basic results and sensitivity test
• 3.2.2 General comparison between models
• 4. Conclusion
• Bibliography
• Appendix A: Mathematical derivation
• Appendix B: Matlab code
• Acknowledgments
• 附件