Solitary Wave and Singular Wave Solutions for Ivancevic Option Pricing Model

Abstract

The nonlinear option pricing model presented by Ivancevic is investigated. By using travelling wave transforming method, the nonlinear option pricing equation is transformed into a differential equation with constant coefficients. By solving the differential equation with F-expansion method, a series of exact solutions have been obtained for the Ivancevic option pricing model. By choosing appropriate parameter values, the dark-soliton and dark-soliton-like solutions, periodic wave solutions, and rogue wave solutions are obtained. These solutions will enrich the types of exact waves in the existing literature of the Ivancevic option pricing model. Furthermore, they may have potential uses in describing the possible physical mechanisms for wave phenomenon in financial markets.

Non-singular complexiton, singular complexiton and complex N-soliton solutions of the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

“…Solitons have important applications in physical and mathematical sciences, such as fluid mechanics, optics, elasticity and plasma science [1][2][3][4][5][6][7][8][9][10][11][12][13]. Recently, many new methods have emerged for exploring the soliton solutions of the PDEs, for instance, the Jacobi elliptic-function technique [14,15], general integral approach [16,17], trial equation approach [18,19], Bäcklund transformation approach [20], exp-function approach [19,21,22], Sardar-subequation method [23][24][25], extended F-expansion approach [26][27][28], Kudryashov's method [29][30][31] and so on [32][33][34][35][36][37][38][39][40][41][42][43][44][45].…”

Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion

“…[18], multiple soliton solutions ranging from king type, single soliton and double soliton to multiple solitons were offered for space-time fractional modified KdV equations. These methods can also be used to obtain soliton, periodical, and rogue wave solutions for the Ivancevic equation [19][20][21][22], which defines the option-pricing wave function in terms of the stock price and time.…”