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. ...
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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.
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 ...
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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.
Ali Safdari-Vaighani; Pooya Garshasebi
Abstract
The financial markets reveal stylized facts that could not be captured by Black-Scholes partial differential equations (PDEs). In this research, we investigate 3/2 stochastic volatility to pricing options which is more compatible with the interpretation of implied volatility. Numerical study and ...
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The financial markets reveal stylized facts that could not be captured by Black-Scholes partial differential equations (PDEs). In this research, we investigate 3/2 stochastic volatility to pricing options which is more compatible with the interpretation of implied volatility. Numerical study and calibrations show that the 3/2 model incorporating jumps effectively encompasses key market characteristics attributed. However, it requires more estimating parameters in comparison to the pure diffusion model. Stochastic volatility models with jumps describe the log return features of the financial market although more parameters are involved in estimations.
