In this paper‎ a combination of two financial derivatives in financial markets modelled of future interest rates is presented and evaluated. In fact ‎European option pricing is driven when zero-coupon bond is considered as underlying asset in a market under Hull-White model‎. ‎For this purpose, the exact solutions of the valuation of this bond option are driven, using Lie group symmetries method. Then in the next part, the finite difference method is applied to find numerical solutions for assumed bond option pricing. Then the significance and usefulness of this approximated method is comparing with the exact solutions by some plotted graphs. پرونده مقاله

In this article, the pricing of option contracts is discussed using the Mikhailov and Nogel model and the artificial neural network method. The purpose of this research is to investigate and compare the performance of various types of activator functions available in artificial neural networks for the pricing of option contracts. The Mikhailov and Nogel model is the same model that is dependent on time. In the design of the artificial neural network required for this research, the parameters of the Mikhailov and Nogel model have been used as network inputs, as well as 700 data from the daily price of stock options available in the Tehran Stock Exchange market (in 2021) as the net-work output. The first 600 data are considered for learning and the remaining data for comparison and conclusion. At first, the pricing is done with 4 commonly used activator functions, and then the results of each are com-pared with the real prices of the Tehran Stock Exchange to determine which item provides a more accurate forecast. The results obtained from this re-search show that among the activator functions available in this research, the ReLU activator function performs better than other activator functions. پرونده مقاله