Option pricing

In this paper we distinguish between operational risks depending on whether the operational risk naturally arises in the context of model risk. As the pricing model exposes itself to operational errors whenever it updates and improves its investment model and other related parameters. In this case, it is no longer optimal to implement the best model. Generally, an option is exercised in a jump-diffusion model, if the stock price either exactly hits the early exercise boundary or the price jumps into the exercise price region. However paths of the diffusion process are continuous. In this paper the impact of operational risk on the option pricing through the implementation of Mitra’s model with jump diffusion model is presented. A partial integral differential equation is derived and the impact of parameters of Merton’s model on operational risk and option value by operational value at risk measure is employed. The option values in the presence of operational risk on data set are computed and some of the results are presented.

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.

Embedded options are virtually new instruments identical to options in many aspects except their non-tradable nature. Testing the efficiency of the Variance Gamma and Black-Scholes-Merton model on these instruments would provide a vision of transitioning from the classical model with its deficiency to more intricate models. Considering the complicated nature of the Variance Gamma stochastic process to price options, the Fast Fourier Transform (FFT) method is used in conjunction with the Nelder-Mead Simplex method to calibrate models. This research uses the Fast Fourier Transform (FFT) to price four embedded options with the ticker symbols Hefars912, Heghadir912, Heksho208, and Hetrol911 under the two models. The result approves that the Variance Gamma process is more efficient than the Black-Scholes-Merton model in pricing embedded options. Consequently, the variance gamma process would generate fewer errors in pricing those options that can be used in a practical sense.