Journal of the Korea Institute of Information and Communication Engineering (한국정보통신학회논문지)

The Korea Institute of Information and Commucation Engineering (한국정보통신학회)
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Option Pricing using Differentiable Neural Networks

미분가능 신경망을 이용한 옵션 가격결정

  • Chi, Sang-Mun (Department of Computer Science, Kyungsung University)
  • Received : 2021.02.01
  • Accepted : 2021.03.08
  • Published : 2021.04.30
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Abstract

Neural networks with differentiable activation functions are differentiable with respect to input variables. We improve the approximation capability of neural networks by using the gradient and Hessian of neural networks to satisfy the differential equations of the problems of interest. We apply differential neural networks to the pricing of financial options, where stochastic differential equations and the Black-Scholes partial differential equation represent the differential relation of price of option and underlying assets, and the first and second derivatives of option price play an important role in financial engineering. The proposed neural network learns - (a) the sample paths of option prices generated by stochastic differential equations and (b) the Black-Scholes equation at each time and asset price. Experimental results show that the proposed method gives accurate option values and the first and second derivatives.

신경망은 미분가능한 활성화 함수를 사용하는 경우에는 입력변수에 대하여 미분가능하다. 본 연구에서는 신경망의 근사 능력을 향상시키기 위하여 신경망의 그래디언트와 헤시안이 블랙-숄즈 미분방정식을 만족하도록 한다. 본 논문은 확률 미분방정식과 블랙-숄즈 편미분 방정식이 옵션 가격과 기초자산의 미분관계를 표현하는 옵션 가격결정에 제안한 방법을 사용한다. 이는 옵션 가격의 일차와 이차미분은 금융공학에서 중요한 역할을 하므로 미분 값을 쉽게 얻을 수 있는 제안한 방법을 적용할 수 있기 때문이다. 제안한 신경망은 (1) 확률 미분방정식이 생성하는 옵션가격의 샘플 경로와 (2) 각 시간과 기초자산 가격에서 블랙-숄즈 방정식을 만족하도록 학습한다. 실험을 통하여 제안한 방법이 옵션가격과 일차와 이차 미분 값을 정확히 예측함을 보인다.

Keywords

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