Optimal Trading Using Black-Scholes Equation with Transaction Costs

Abstract

This work deals with optimal trading using Black-Scholes equation with transaction costs. The partial differential equation for option pricing with transaction costs on the domain (P,T)∈(0,∞)×(0,T) with terminal condition C(P,T)=Max(P-E,0),P∈(0,∞) for European call options with strike price, E, and a suitable terminal condition for European puts was obtained and then solved to obtain the optimal value function.

A Numerical Approximation on Black-Scholes Equation of Option Pricing

“…Where r represents interest rate, t  represents continuous dividend yield, The details of the above option model can be expressly found in the following books: [15,16] and [17][18] etc. However, Black-Scholes model is based on seven assumptions:…”

“…The maturity period, and the option are well computed for all the different initial stock prices using a boundary conditions for uniqueness of solution. To get the prices at , the model solves backwards for every time step from ," [17], [11,12,18].…”

New Solutions of Time- and Space-Fractional Black–Scholes European Option Pricing Model via Fractional Extension of He-Aboodh Algorithm

“…Te classical Black-Scholes equation was originated to determine the theoretical value of an option contract using current stock prices, the option's strike price, expected dividends, time of expiration, expected interest rates, and volatility. Some other modifcations of Black-Scholes models have been suggested that are the jump-difusion model [6], transaction cost models [7,8], stochastic interest model [9], and stochastic volatility model [10]. After the fractal structures for the fnancial market [11] were discovered, the standard Brownian motion of the classical Black-Scholes equation was replaced by fractional Brownian motion to obtain the fractional Black-Scholes model.…”