AJOU Central Library Repository: Solving Black-Scholes PDE associated with Local Volatility via Physics-Informed Neural Network

Graduate School of Ajou University Department of Financial Engineering 3. Theses(Master)

Solving Black-Scholes PDE associated with Local Volatility via Physics-Informed Neural Network

Keyword: Black-Scholes PDE; Deep Learning; Dupire’s equation; Local volatility; Option Pricing; parametric PDE

Alternative Abstract: 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.

Appears in Collections:: Graduate School of Ajou University > Department of Financial Engineering > 3. Theses(Master)

qrcode

STATISTICS: Total Visit :4,040,573; Total Download :1,962; Today View :6,624

AJOU Central Library Repository는 국립중앙도서관 OAK 보급사업으로 구축되었습니다.