IJPAM: Volume 119, No. 4 (2018)

Title

ESTIMATION OF THE BASIC STOCK OPTION PARAMETERS
IN THE SENSE OF ITO STOCHASTIC DYNAMICS

Authors

S.O. Edeki$^1$, M.E. Adeosun$^2$, G.O. Akinlabi$^3$,
I. Adinya$^4$, J.I. Ejiogu$^5$
$^{1,3,5}$Department of Mathematics
Covenant University
Canaanland, Ota, NIGERIA
$^2$Department of Mathematics and Statistics
Osun State College of Technology
Esa-Oke, NIGERIA
$^4$Department of Mathematics
University of Ibadan
Ibadan, NIGERIA

Abstract

In this paper, stock price basic parameters: expected value and volatility are being estimated in the sense of Ito stochastic dynamics. For model efficiency, stock exchange data of DBS Group Holding Ltd (D05. SI) spanning between May 23, 2010 to May 15, 2016 (weekly data with 312 sample size) are considered. It is remarked that the data, and the proposed models have many applications in financial institutions, and other areas of applied sciences.

History

Received: December 8, 2017
Revised: May 10, 2018
Published: July 29, 2018

AMS Classification, Key Words

AMS Subject Classification: 91B25, 93E35
Key Words and Phrases: option pricing, stochastic model, Ito calculus, Black-Scholes model, stock exchange market

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
L. Bachelier, Theorie de la Speculative, Paris: Gauthier- Villar. Translated in Cooler, (1964).

2
F. Black F, P. Karasinki, Bond and option pricing when short rates lognormal, Finan. Analysis J., 47 (4), (1991), 52-59.

3
F. Black, M. Scholes, The pricing of options and corporate liability, J. Political Economy, 81, (1973), 637-659.

4
J. Hull , A. White, The pricing of options on assets with stochastic volatility, J. Finance, 42, (1987), 271-301.

5
S. Susumu, H. Mijuki, An improvement in the stochastic stock price differences Model, Journal of Applied Operational Research., 4 (3), (2012), 125-138.

6
J.P. McNicholas, J.L. Rzzo, Stochastic GBM Methods for Modelling Market Prices, Casuality Actuarial Society E-Forum, Summer (2012).

7
S. O. Edeki, I. Adinya, O. O. Ugbebor, The Effect of Stochastic Capital Reserve on Actuarial Risk Analysis via an Integro-differential Equation, IAENG International Journal of Applied Mathematics, vol. 44 (2), (2014), 83-90.

8
M. E. Adeosun, S. O. Edeki, O.O. Ugbebor, Stochastic Analysis of Stock Market Price Models: A Case Study of the Nigerian Stock Exchange (NSE), WSEAS Transactions on Mathematics, 14, (2015), 353-363.

9
R. S. Sorin, Stochastic modeling of stock prices, Mongometry investment technology Inc. 200 Federal Street Camden, NJ 08103, (1997).

10
S. O. Edeki, M.E. Adeosun, E.A. Owoloko, G.O. Akinlabi, I. Adinya, Parameter Estimation of Local Volatility in Currency Option Valuation, International Review on Modelling and Simulations (IREMOS), 9 (2), (2016), 130-133. https://doi.org/10.15866/iremos.v9i2.8161.

11
https://sg.finance.yahoo.com/quote/D05.SI/history?period1.

12
S. O. Edeki, and O.O. Ugbebor, On a Generalized Squared Gaussian Diffusion Model for Option Valuation, MATEC Web of Conferences, 125, 02015, (2017).

13
S.O. Edeki, O.O. Ugbebor, E.A. Owoloko, On a Nonlinear Transaction-Cost Model for Stock Prices in an Illiquid Market Driven by a Relaxed Black-Scholes Model Assumptions, Malaysian Journal of Mathematical Sciences, 11 (1), (2017), 83 - 96.

14
G. Wang, X. Wang . K. Zhoui, Pricing vulnerable options with stochastic volatility, Physica A 485, (2017), 91-103.

15
S. O. Edeki, O. O. Ugbebor, E.A. Owoloko, On a Dividend-Paying Stock Options Pricing Model (SOPM) Using Constant Elasticity of Variance Stochastic Dynamics, International Journal of Pure and Applied Mathematics, 106 (4), (2016), 1029-1036.

16
L. Panzar, E.C. Cipu, Using of stochastic Ito and Stratonovich integrals derived security pricing, Proceedings of The 3-rd International Colloquium. Mathematics in Engineering and Numerical Physics, October 7-9, Bucharest, Romania, (2004), 222-229.Luigi T. De Luca, Propulsion physics (EDP Sciences, Les Ulis, 2009).

17
S.O. Edeki, E.A. Owoloko, and O.O. Ugbebor, The Modified Black-Scholes Model via Constant Elasticity of Variance for Stock Options Valuation, AIP Conference proceedings, 1705, 020041 (2016); doi: 10.1063/1.4940289.

How to Cite?

DOI: 10.12732/ijpam.v119i4.8 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2018
Volume: 119
Issue: 4
Pages: 661 - 668


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).