Mohammad Reza Haddadi; Hossein Nasrollahi
Abstract
In order to reduce the risk of financial markets, various tools have emerged, and option contracts are the most common tools in this regard. The Black-Scholes model is used to price a wide range of options contracts. The basic assumption in this model is to follow the normal distribution of returns. ...
Read More
In order to reduce the risk of financial markets, various tools have emerged, and option contracts are the most common tools in this regard. The Black-Scholes model is used to price a wide range of options contracts. The basic assumption in this model is to follow the normal distribution of returns. But the reality of the market indicates the skewness and kurtosis of the data, which reduces the accuracy of calculating the option price. The Gram-Charlie model has more flexibility than Black-Scholes model with abnormal skewness and kurtosis. The main purpose of this research is to determine the European call option price using non-normal data. In this regard, we present new models, fractional Gram-Charlier model and mixed fractional Gram-Charlier model, for option pricing. For this purpose, the data of Shasta and Khodro symbols have been selected from Iran Stock Exchange that Khodro in the period 2020-07-27 to 2023-11-1 and Shasta in the period 2022-7-25 to 2023-11-1 have been used. The results of this research show that Shasta has more abnormal skewness and kurtosis than Khodro. The option price calculated with the Gram-Charlier and extended models of Gram-Charlier are shown a smaller error compared to other models in the Shasta. Also, the results show that under abnormal skewness and kurtosis, our new models have more flexibility than the Black-Scholes model and fractional models.
Behzad Abbasi; Kazem Nouri
Abstract
Option pricing is a fundamental issue in financial markets, and barrier options are a popular type of options that can become valuable or worthless when the underlying asset price reaches a predetermined level. A double barrier option consist two barriers, one situated above and the other below the prevailing ...
Read More
Option pricing is a fundamental issue in financial markets, and barrier options are a popular type of options that can become valuable or worthless when the underlying asset price reaches a predetermined level. A double barrier option consist two barriers, one situated above and the other below the prevailing stock price. This particular option is categorized as path dependent because the return for the holder is influenced by the stock price’s breach of the two barriers. The double barrier option contract stipulates three specific payoffs, depending on whether the up-barrier or down-barrier is touched, or if there is no breach of either barrier during the entire duration of the option. In this paper, pricing of the double barrier options when the underlying asset price follows the exponential Ornstein-Uhlenbeck model is investigated, and also pricing formulas for different types of double barrier options (knock-in and knock-out) are derived by α-paths of uncertain differential equations in the uncertain environment.
Saeed Vahdati; Foad Shokrollahi
Abstract
This article proposes a new numerical technique for pricing asset-or-nothing options using the Black-Scholes partial differential equation (PDE). We first use the θ−weighted method to discretize the time domain, and then use Haar wavelets to approximate the functions and derivatives with ...
Read More
This article proposes a new numerical technique for pricing asset-or-nothing options using the Black-Scholes partial differential equation (PDE). We first use the θ−weighted method to discretize the time domain, and then use Haar wavelets to approximate the functions and derivatives with respect to the asset price variable. By using some vector and matrix calculations, we reduce the PDE to a system of linear equations that can be solved at each time step for different asset prices. We perform an error analysis to show the convergence of our technique. We also provide some numerical examples to compare our technique with some existing methods and to demonstrate its efficiency and accuracy.
Farshid Mehrdoust; Maryam Noorani
Abstract
This study suggests a novel approach for calibrating European option pricing model by a hybrid model based on the optimized artificial neural network and Black-Scholes model. In this model, the inputs of the artificial neural network are the Black-Scholes equations with different ...
Read More
This study suggests a novel approach for calibrating European option pricing model by a hybrid model based on the optimized artificial neural network and Black-Scholes model. In this model, the inputs of the artificial neural network are the Black-Scholes equations with different maturity dates and strike prices. The presented calibration process involves training the neural network on historical option prices and adjusting its parameters using the Levenberg-Marquardt optimization algorithm. The resulting hybrid model shows superior accuracy and efficiency in option pricing on both in sample and out of sample dataset.
Ali Bolfake; Seyed Nourollah Mousavi; Sima Mashayekhi
Abstract
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, ...
Read More
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.
Azadeh Ghasemifard; Seddigheh Banihashemi; Afshin Babaei
Abstract
The aim of this paper is to numerically price the European double barrier option by calculating the governing fractional Black-Scholes equation in illiquid markets. Incorporating the price impact into the underlying asset dynamic, which means that trading strategies affect the ...
Read More
The aim of this paper is to numerically price the European double barrier option by calculating the governing fractional Black-Scholes equation in illiquid markets. Incorporating the price impact into the underlying asset dynamic, which means that trading strategies affect the underlying price, we consider markets with finite liquidity. We survey both cases of first-order feedback and full feedback. Asset evolution satisfies a stochastic differential equation with fractional noise, which is more realistic in markets with statistical dependence. Moreover, the Sinc-collocation method is used to price the option. Numerical experiments show that the results highly correspond to our expectation of illiquid markets.
