Numerical Solving the Black-Scholes Equation under the Constant Elasticity of Variance Model Using Laguerre Neural Network

The classical Black-Scholes equation is one of the most important mathematical models in option pricing theory, but this model is far from market realities and cannot show the inverse relationship between the stock price and its volatility in the market. Also, Black and Scholes supposed that no dividends are paid on underlying assets during that period. Therefore, we suppose that dividend yeild is paid on stock during that period. This paper investigates a European put option price based on the constant elasticity of variance (CEV) model, which parameters of interest rate and dividend yield supposed as deterministic functions of time. This model does not have a closed-form solution. Hence, we numerically valuate the European option price by using a nonparametric method. To this end, we consider the neural network, which is one of the most powerful learning methods. In this paper, we study a neural network algorithm based on Laguerre polynomials for solving the generalized Black-Scholes equation arising in the financial market.

کلیدواژه ها:

Neural network ، Approximate solutions ، Black-Scholes equation ، CEV model ، Opion price.