Abdolsadeh Neisy
Kimiya Tavakoli; Abdolsadeh Neisy; Alireza Zamanpour
Abstract
Modeling and pricing European options are crucial tasks for financial companies seeking to determine the fair value of these instruments. Conventional methods, such as using Black-Scholes partial differential equations (PDEs), face challenges due to the high complexity involved and lack of data. To address ...
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Modeling and pricing European options are crucial tasks for financial companies seeking to determine the fair value of these instruments. Conventional methods, such as using Black-Scholes partial differential equations (PDEs), face challenges due to the high complexity involved and lack of data. To address these challenges, PINNs have recently emerged as a promising approach to solving the Black-Scholes PDEs for European options. In this paper, we tackle the two-dimensional Black-Scholes model to determine the price of a European exchange option. We employ a kind of ANNs (PINN) that is specifically designed to learn the option’s value by minimizing an appropriately defined loss function. The data for our study were generated through simulations conducted in Python. Our results demonstrate the efficacy of the PINN approach by comparing the computed fair value of a European exchange option with the traditional solutions. The findings underscore the potential of PINNs in providing accurate and efficient pricing for complex financial derivatives.
Abdolsadeh Neisy; Nasrollah Mahmoudpour; Moslem Peymany; Meisam Amiri
Abstract
Pricing catastrophe swap as an instrument for insurance companies risk management, has received trivial attention in the previous studies, but in most of them, damage severities caused by the disaster has been considered to be fixed. In this study, through considering jumps for modeling the occurrence ...
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Pricing catastrophe swap as an instrument for insurance companies risk management, has received trivial attention in the previous studies, but in most of them, damage severities caused by the disaster has been considered to be fixed. In this study, through considering jumps for modeling the occurrence of disasters as in Unger [32] and completing it through considering damages caused by natural disasters as stochastic, an integro-differential model was extracted to value catastrophe swap contracts. In determining the swap price changes, the Ito command was followed and to achieve the catastrophic swap model, the generalization of the Black and Scholes modeling method was used. [3]. With regard to the initial and boundary conditions, extracted model does not have an analytical solution; thus, its answer was approximated using the finite difference numerical method and the effect of considering the damage as stochastic on swap value was analyzed. In addition, the model and the extracted numerical solution were separately implemented on the data about the earthquake damage in the United States and Iran. The results showed that prices will experience a regular upward trend until damage growth, damage severities, and occurrence probability of a catastrophe are not so high that the buyer of the swap is forced to pay compensation to the swap’s seller. Of course, the prices will fall sharply as soon as they reach and cross the threshold.
Sedighe sharifian; Ali R. Soheili; Abdolsadeh Neisy
Abstract
The bond market is an important part of the financial markets . The coupon bonds are issued by companies or banks for increasing capital , and the interest is paid by banks or companies, periodically . In terms of maturities , bonds are divided ...
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The bond market is an important part of the financial markets . The coupon bonds are issued by companies or banks for increasing capital , and the interest is paid by banks or companies, periodically . In terms of maturities , bonds are divided into three categories as follows : short term , medium term , and long term .In this paper , we model the fractional bond pricing under fractional stochastic differential equation . We implement the multiquadric approximation for solving the fractional bond pricing equation . The equation is discretized in the time direction base on modified Riemann-- Liouville derivative and finite difference methods and is approximated by using the multiquadric approximation method in the space direction which achives the semi-- discrete solution . We investigate the unconditional stability and convergence of the proposed method. Numerical results demonstrate the efficiency and ability of the presented method .
Mehrdokht Khani; Abdolsadeh Neisy
Abstract
In this paper, we first present a nonlinear structural model for pricing mortgage-backed securities. These derivatives are considered to be the primary cause of the 2008 financial crisis that was raised in the United States. We focus our work on pass-through mortgages, which pay both the principal and ...
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In this paper, we first present a nonlinear structural model for pricing mortgage-backed securities. These derivatives are considered to be the primary cause of the 2008 financial crisis that was raised in the United States. We focus our work on pass-through mortgages, which pay both the principal and interest to the investors. We begin our work by introducing the factors that affect the market of mortgage-backed securities. Then, by applying some assumptions and conditions to the parameters of the initial model, and without the loss of generality, we show that this model can be greatly simplified. We focus our attention on how the change in interest rates can affect the value of mortgage-backed securities. Various numerical methods can be used to solve the reduced model that is achieved. We adapt the mesh-less method of radial basis functions to solve the reduced model. The numerical results indicate that the method that we have used can capture the market trends in a specific interval.
