scholarly journals The Lie Algebraic Approach for Determining Pricing for Trade Account Options

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 279
Author(s):  
Shih-Hsien Tseng ◽  
Tien Son Nguyen ◽  
Ruei-Ci Wang
Keyword(s):  
Option Pricing ◽  
Analytical Solutions ◽  
Algebraic Approach ◽  
Lie Symmetry ◽  
Lie Theory ◽  
Lie Symmetry Analysis ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Trade Account ◽  
Pricing Problems

In recent years, many advanced techniques have been applied to financial problems; however, very few scholars have used the Lie theory. The purpose of this study was to examine the options for a trade account through Lie symmetry analysis. According to our results, it is effective for determining analytical solutions for pricing issues and solving other partial differential equations. The proposed solution can be used by further researchers or practitioners in option pricing problems for better performance compared with the classical Black–Scholes model.

scholarly journals Lie Symmetry Analysis of a First-Order Feedback Model of Option Pricing

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Winter Sinkala ◽  
Tembinkosi F. Nkalashe
Keyword(s):  
Option Pricing ◽  
Coupled System ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
First Order ◽  
Feedback Model ◽  
Black Scholes Model ◽  
Black Scholes

A first-order feedback model of option pricing consisting of a coupled system of two PDEs, a nonliner generalised Black-Scholes equation and the classical Black-Scholes equation, is studied using Lie symmetry analysis. This model arises as an extension of the classical Black-Scholes model when liquidity is incorporated into the market. We compute the admitted Lie point symmetries of the system and construct an optimal system of the associated one-dimensional subalgebras. We also construct some invariant solutions of the model.

scholarly journals PREFERENCES, LÉVY JUMPS AND OPTION PRICING

2007 ◽  
Vol 03 (01) ◽  
pp. 0750001 ◽  
Author(s):  
CHENGHU MA
Keyword(s):  
Option Pricing ◽  
Contingent Claims ◽  
Economic Variable ◽  
European Options ◽  
Jump Risk ◽  
Representative Agent ◽  
Potential Explanation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Lévy Jumps

This paper derives an equilibrium formula for pricing European options and other contingent claims which allows incorporating impacts of several important economic variable on security prices including, among others, representative agent preferences, future volatility and rare jump events. The derived formulae is general and flexible enough to include some important option pricing formulae in the literature, such as Black–Scholes, Naik–Lee, Cox–Ross and Merton option pricing formulae. The existence of jump risk as a potential explanation of the moneyness biases associated with the Black–Scholes model is explored.

Option pricing models

1989 ◽  
Vol 116 (3) ◽  
pp. 537-558 ◽  
Author(s):  
D. Blake
Keyword(s):  
Option Pricing ◽  
Binomial Model ◽  
Pricing Models ◽  
Black Scholes Model ◽  
Black Scholes

ABSTRACTThe paper discusses two important models of option pricing: the binomial model and the Black—Scholes model. It begins with a brief description of options.

scholarly journals Markov Chain Monte Carlo Method for Estimating Implied Volatility in Option Pricing

2018 ◽  
Vol 10 (6) ◽  
pp. 108
Author(s):  
Yao Elikem Ayekple ◽  
Charles Kofi Tetteh ◽  
Prince Kwaku Fefemwole
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Call Option ◽  
Option Prices ◽  
Options Market ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Real Market ◽  
Independent Path

Using market covered European call option prices, the Independence Metropolis-Hastings Sampler algorithm for estimating Implied volatility in option pricing was proposed. This algorithm has an acceptance criteria which facilitate accurate approximation of this volatility from an independent path in the Black Scholes Model, from a set of finite data observation from the stock market. Assuming the underlying asset indeed follow the geometric brownian motion, inverted version of the Black Scholes model was used to approximate this Implied Volatility which was not directly seen in the real market: for which the BS model assumes the volatility to be a constant. Moreover, it is demonstrated that, the Implied Volatility from the options market tends to overstate or understate the actual expectation of the market. In addition, a 3-month market Covered European call option data, from 30 different stock companies was acquired from Optionistic.Com, which was used to estimate the Implied volatility. This accurately approximate the actual expectation of the market with low standard errors ranging between 0.0035 to 0.0275.

scholarly journals Finite Difference/Fourier Spectral for a Time Fractional Black–Scholes Model with Option Pricing

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Juan He ◽  
Aiqing Zhang
Keyword(s):  
Option Pricing ◽  
Dynamic Behavior ◽  
Numerical Scheme ◽  
Step Size ◽  
Spatial Direction ◽  
Discrete Method ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Difference Fourier ◽  
The Impact

We study the fractional Black–Scholes model (FBSM) of option pricing in the fractal transmission system. In this work, we develop a full-discrete numerical scheme to investigate the dynamic behavior of FBSM. The proposed scheme implements a known L1 formula for the α-order fractional derivative and Fourier-spectral method for the discretization of spatial direction. Energy analysis indicates that the constructed discrete method is unconditionally stable. Error estimate indicates that the 2−α-order formula in time and the spectral approximation in space is convergent with order OΔt2−α+N1−m, where m is the regularity of u and Δt and N are step size of time and degree, respectively. Several numerical results are proposed to confirm the accuracy and stability of the numerical scheme. At last, the present method is used to investigate the dynamic behavior of FBSM as well as the impact of different parameters.

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