Option pricing model is a wildly interested topic in an area of financial Mathematics. The pioneer model was introduced by Fischer Black and Myron Scholes which is known as the Black-Scholes model. This model was derived under various assumptions such as liquidity and no transaction costs for which a underlying asset price in stock market might not be satisfied. With this fact, the underlying asset price models were remodeled, in order to determine an option value. This research aims to extend the Black-Scholes model by relaxing the assumption of no transaction costs in illiquid markets. Also, jumps of asset price are considered in this work. To do this, a differential form of asset price with transaction costs and jumps in illiquid markets is introduced and then used to construct the extended option pricing model. Furthermore, a numerical result of a call option price under a new situation is provided.
References
[1]
Black, F. and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81, 637-654. https://doi.org/10.1086/260062
[2]
Dokuchaev, N.G. and Savkin, A.V. (1998) The Pricing of Options in a Financial Market Model with Transaction Costs and Uncertain Volatility. Journal of Multinational Financial Management, 8, 353-364. https://doi.org/10.1016/S1042-444X(98)00036-X
[3]
Florescu, I., Mariant, M.C. and Sengupta, I. (2014) Option Pricing with Transaction Costs and Stochastic Volatility. Electronic Journal of Differential Equations, 2014, 1-19.
[4]
FEdeki, S.O., Ugbebor, O.O. and Owoloko, E.A. (2017) On a Nonlinear Transaction-Cost Model for Stock Prices in an Illiquid Market Driven by a Relaxed Black-Scholes Model Assumption. Malaysian Journal of Mathematical Sciences, 11, 83-96.
[5]
Liu, H. and Yong, J. (2005) Option Pricing with an Illiquid Asset Market. Journal of Economic Dynamics & Control, 29, 2125-2156. https://doi.org/10.1016/j.jedc.2004.11.004
[6]
Glover, K.J., Duck, P.W. and Newton, D.P. (2010) On Nonlinear Models of Markets with Finite Liquidity: Some Cautionary Notes. SIAM Journal on Applied Mathematics, 70, 3252-3271. https://doi.org/10.1137/080736119
[7]
Pirvu, T.A. and Yazdanian, A. (2015) Numerical Analysis for Spread Option Pricing Model in Illiquid underlying Asset Market: Full Feedback Model. Applied Mathematics & Information Sciences, 1271-1281. https://doi.org/10.18576/amis/100406
[8]
El-Khatib, Y. and Hatemi-J, A. (2013) On Option Pricing in Illiquid Markets with Jumps. International Scholarly Research Notices, 2013, Article ID 567071. https://doi.org/10.1155/2013/567071
[9]
Agana, F., Makinde, O.D. and Theuri, D.M. (2016) Numerical Treatment of a Generalized Black-Scholes Model for Options Pricing in an Illiquid Financial Market with Transections Costs. Global Journal of Pure and Applied Mathematics, 12, 4349-4361.
[10]
Rouah, F. (2013) Four Derivations of the Black Scholes PDE. http://frouah.com/finance%20notes/Black%20Scholes%20PDE.pdf
[11]
Mukam, J.D. (2015) Stochastic Calculus with Jumps Processes: Theory and Numerical Techniques. M.S. Dissertation, African Institute for Mathematical Sciences (AIMS) Senegal.
