ELS pricing with Physics-informed neural network
- 주제(키워드) Black-Scholesequation , Physics-informedneuralnetwork(PINN) , Opera- tor SplittingMethod(OSM) , MonteCarlosimulation(MC)
- 주제(DDC) 332
- 발행기관 아주대학교
- 지도교수 배형옥
- 발행년도 2023
- 학위수여년월 2023. 2
- 학위명 석사
- 학과 및 전공 일반대학원 금융공학과
- 실제URI http://www.dcollection.net/handler/ajou/000000032795
- 본문언어 영어
- 저작권 아주대학교 논문은 저작권에 의해 보호받습니다.
초록/요약
Equity linked securities(ELS) are securities whose returns on investment are tied to the returns of individual stocks or equity indices. It is important to calculate theoretical prices and Greeks of ELS because they have a significant impact on decision-making of investor and hedging strategy of the issuer. In finance, Monte-Carlo simulation(MC) and partial differential equations are being used for financial derivatives pricing. Among the partial differential equation approaches, the finite difference method(FDM) is the most used numerical method to solve Black-Scholes equation. As one of the finite difference methods, operator splitting method(OSM) is mainly used to solve a multidimensional Black-Scholes equation. In this paper, we apply physics-informed neural network(PINN) to the multidimensional Black-scholes equation and calculate theoretical price of a step-down ELS which has two underlying assets. Then we compare with the price with OSM and MC. Also, we calculate Greeks of ELS with PINN and compare those of OSM.
more목차
I Introduction 1
II Background 3
1 Black-Scholes Model 3
2 Monte Carlo Simulation 6
(a) Sampling procedure 6
(b) Cholesky decomposition 7
3 Finite Difference Method 8
(a) Operator Splitting Method 8
(b) Tridiagonal matrix algorithm 10
IIIPhysics-informed Neural Network for ELS pricing 11
1 Physics-informed Neural Network 11
2 2 Asset Step-Down ELS 12
(a) Overview of 2 Asset step-down ELS 12
(b) Initial and boundary conditions for ELS 14
3 Physics-informed neural network for ELS pricing 16
(a) Scale invariance of Black-Scholes model 16
(b) Optimization problem 17
IV Numerical Simulation 21
1 Price 22
2 Greeks 24
V Conclusion 28
