Solving Black-Scholes PDE associated with Local Volatility via Physics-Informed Neural Network
- 주제(키워드) Option Pricing , Local volatility , Deep Learning , Black-Scholes PDE , parametric PDE , Dupire’s equation
- 주제(DDC) 332
- 발행기관 아주대학교
- 지도교수 배형옥
- 발행년도 2021
- 학위수여년월 2021. 8
- 학위명 석사
- 학과 및 전공 일반대학원 금융공학과
- 실제URI http://www.dcollection.net/handler/ajou/000000031023
- 본문언어 영어
- 저작권 아주대학교 논문은 저작권에 의해 보호받습니다.
초록/요약
In this article, we solve the Black-Scholes Partial Difference Equation(BS PDE) under the local volatility model by using an artificial neural network, and obtain the price and the greeks of derivatives in forms of function simultaneously. Dupire’s local volatility model is one of the most successful for equity models. In practice, it is important to price and hedge derivatives under the local volatility model. We provide an artificial neural network scheme for efficiently solving parametric PDEs. We adopt local volatility models, especially, constant elasticity of variance(CEV) model and volatility surface. The price function of European vanilla options under the local volatility model satisfies Dupire's equation. We solve the parametric PDE of the European put option under the local volatility model with an artificial neural network and show that solution and Dupire's equation are approximated.
more목차
1. Introduction 1
2. Local Volatility model 2
2.1 Geometric Brownian Motion 3
2.2 Constant Elasticity of Variance model 4
2.3 Volatility surface 7
3. Neural Networks for PDE solver 8
3.1 Current Research and Related Work 8
3.2 Neural Networks for Local Volatility Black-Scholes PDE 9
3.3 Transfer learning 10
4. Numerical results 11
4.1 GBM 12
4.2 CEV model 16
4.3 Volatility surface 25
5. Conclusion 28
References 29
