In this paper, we present a new version of the DOUBLE HESTON model, where the mixed Duffie-Kan model is used to predict the volatility of the model instead of the CIR process. According to this model, we predict the stock price and calculate the European option price by using the Monte-Carlo method. Finally, by applying the proposed model, we find the optimal portfolio under the Cardinality Constraints Mean–, Variance (CCMV) model and compare it with the mixed DOUBLE Houston model and show its efficiency.

Objective The significance of the capital market in driving the economic growth and development of a country necessitates a thorough examination of this market from multiple perspectives. Participating in this market invariably involves a heightened level of risk, prompting the emergence of various tools aimed at mitigating these risks. One of the main factors affecting investment decisions is the accurate valuation of derivatives, including options. The Black-Scholes model is used to price a wide range of options contracts. The basic assumption in this fixed model is to consider volatility, which reduces the accuracy of calculating the option price. The main purpose of this research is to determine the price of a European call option with stochastic volatility.   Methods The HESTON-Nandi model is a closed pricing formula for European options that shares numerous assumptions with the HESTON model. The main difference between the HESTON-Nandy model and the Black-Scholes model is the use of the variance type when option pricing. The HESTON-Nandy model considers the non-normal distribution of returns and random fluctuations more realistically. Since the HESTON model is one of the effective models among the random turbulence models, in this study, the option pricing under HESTON and HESTON Nandi random stochastic is discussed, which has been investigated considering the non-normality of the data distribution.   Results In this study, data from Iran Khodro was utilized, spanning the period from November 21, 2020, to December 14, 2022. To increase the accuracy, the volatility was calculated using two historical and implied methods. Following the application of option pricing using all three models, namely Black-Scholes, HESTON, and HESTON-Nandi, and subsequent comparison of the results, it was determined that the HESTON-Nandi model exhibited superior performance when compared to the other two models.   Conclusion The findings of this research indicate that, in both the short, medium, and long terms, the HESTON-Nandi model yields prices that closely align with market prices and exhibits lower error rates. Consequently, it can be inferred that the HESTON-Nandi model demonstrates a high degree of flexibility. The HESTON-Nandi model outperforms the Black-Scholes and HESTON models by capturing unusual patterns like skewness and elongation. This makes it a good alternative to those models.

Objective: In this paper, while introducing HESTON's model of stochastic variance, regarding the jump process and the long-term memory feature of prices, a new model for pricing subordinate shares is presented. In the following, the performance of this model is discussed in comparison to the two other models of random variance, HESTON and Bates. Methods: In this research, the Fractional-Jump HESTON Model has been created through combining the jump process and Hurst exponent. The new model has been generated while the long-term memory characteristics of the stock market price trends and the vulnerability of prices in response to sudden changes have been taken into consideration. Then we have determined the characteristic function of the underlying asset price process in the new model, which has been used to derive a formula for subordinate shares pricing using the Monte Carlo method and the variance reduction technique. Results: To test and Compare the option pricing models, we have used the subordinate shares data during 2012-2017. After calibrating and pricing subordinate shares by all three models and comparing the results, it was found that the Fractional-Jump HESTON model has a better performance than the other two models in terms of the valuation of Tabai options. Conclusion: The comparison results show that the estimation by the Fractional-Jump HESTON model is closer to the actual results of the subordinate shares’ prices, and is better than the two well-known models of stochastic variance, HESTON and Bates.

This paper proposes a new approach to pricing European options using deep learning techniques under the HESTON and Bates models of random fluctuations. The deep learning network is trained with eight input hyper-parameters and three hidden layers, and evaluated using mean squared error, correlation coefficient, coefficient of determination, and computation time. The generation of data was accomplished through the use of Monte Carlo simulation, employing variance reduction techniques. The results demonstrate that deep learning is an accurate and efficient tool for option pricing, particularly under challenging pricing models like HESTON and Bates, which lack a closed-form solution. These findings highlight the potential of deep learning as a valuable tool for option pricing in financial markets.

The purpose of this study is to investigate the effects and risk spillover from the global crude oil market on Tehran Stock Exchange Oil Group. For this purpose, we used a combination of copula models and switching models in this research. First, we will examine marginal models and examine HESTON switching and Markov switching models in this market. Then we create the multivariate distribution function using Clayton's copula. The data analyzed in this research are related to the global crude oil markets and the Tehran Stock Exchange Oil Group from December 2011 to January 2023. This time period was chosen due to the examination of different regimes in the above markets and also the selection of the appropriate marginal model for these markets. The results show the crude oil market has influenced on Tehran Stock Exchange and also the Tehran Stock Exchange Oil Group indices. Volatility in this global market cause turbulence in the Tehran stock market and this market is affected by the global crude oil market. This is due to the influence of the global crude oil market on total prices in these markets. HESTON switching model and its combination with copula models including Clayton copula can bring good results. This is confirmed by comparing this model with other models such as copula Markov switching models.

In this paper, power option pricing is driven applying by daily information of Tehran stock exchange. The sample period of the study is from 1387 to 1397, when Tehran stock exchange index is approximately closed to HESTON model. In this work, the considered pricing is done in two sections with different period of times. At first, The fast Fourier transform is applied for solving our main model. In the sequel the results of the considered pricing are shown that power option pricing can not follow the HESTON model that means it causes the arbitrage situations in our considered market, Tehran stock exchange.

In this study, overall index of Tehran Stock Exchange is modeled by HESTON stochastic differential equations and its performance is measured. To do this, after a brief introduction of stochastic differential equations, HESTON model is explained in more detail and parameters of this model based on the data of Tehran Stock Exchange overall index is estimated. In this way, Fokker-Plank theorem is used to find probability distribution function of HESTON model and Gauss-Hermit method is used to estimate an indefinite integral. Finally we calculate value at risk of Tehran Stock Exchange overall index by Monte Carlo methods based on HESTON model and we compare this with Geometric Brownian model as a widely used model by means of back test approach. These tests show superior performance of HESTON model.