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.
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.
