Evaluation of Various Numerical Methods for Option Pricing Model

Fischer Black and Myron Scholes derive partial differential equations and are now called Black-Scholes equations and control the price of options. An important idea is to "hide the risk" by trading the underlying assets to hedge the options completely. Many empirical tests showed that the price of Black Scholes is quite close to the observed price. This formula caused a boom in option trading and legalized the activities of the global option market.

In recent years, option valuation method is very important in monetary theory, and in fact it has increased significantly. Various methods of option price evaluation include binary tree model, Monte Carlo simulation, and difference method. The two-person model was proposed by Cox, Ross and Rubinstein (1979). Boyle (1977) first discussed the Monte Carlo simulation. It was then used to evaluate the choice when Johnson and Shanno (1985) and Hull and White (1987) are random processes. Schwartz (1977), Brennan and Schwartz (1979) and Courtadon (1982) (Hull and White, 1988) discuss differential methods. This paper aims to provide comparison and comparison of the above three numerical methods. All of these numerical methods focus on the goal of calculating accuracy and speed. The only way to achieve higher accuracy and speed in a given way is multiple computation (Hull and White, 1988).

In recent years, numerical methods for evaluating options such as binomial tree model, Monte Carlo simulation, and difference method are used for a wide range of monetary purposes. This paper describes and compares three numerical methods. On the one hand we will outline three ways of defining three ways, advantages and disadvantages, and the determinants of each method. On the other hand, this paper concretely compares the selection of three numerical methods. In general, three numerical methods have proved to be valuable and effective ways to evaluate alternatives.

Introduction: Digital models are an important tool for designing, adjusting, and evaluating several methods in various image processing applications, such as echocardiography and mammography. We propose a framework for creating ultrasonic numerical deformation model based on finite element method (FEM), linear isomorphism, and field II. Since the proposed method considers the scatterer map to be a characteristic of tissue, the scatterer should move according to tissue distortion. How to do: First, load the volume that represents the target organization. Next, parameter values ​​such as Young's modulus, scatterer density, attenuation, and scattering amplitude are inserted for each different region of the phantom. Other parameters associated with the ultrasonic device, such as ultrasonic frequency and the number of transducer elements, are then also defined to perform ultrasonic acquisition using field II. After that, FEM is executed and deformation is calculated. (Author)