Edeki, S.O. and Covenant University, Theses (2017) ANALYTICAL STUDY AND GENERALISATION OF SELECTED STOCK OPTION VALUATION MODELS. Masters thesis, COVENANT UNIVERSITY.
![[img]](http://eprints.covenantuniversity.edu.ng/style/images/fileicons/application_pdf.png) |
PDF
Download (4MB) |
Abstract
In this work, the classical Black-Scholes model for stock option valuation on the basis of some stochastic dynamics was considered. As a result, a stock option val- uation model with a non-�xed constant drift coe�cient was derived. The classical Black-Scholes model was generalised via the application of the Constant Elasticity of Variance Model (CEVM) with regard to two cases: case one was without a dividend yield parameter while case two was with a dividend yield parameter. In both cases, the volatility of the stock price was shown to be a non-constant power function of the underlying stock price and the elasticity parameter unlike the constant volatility assumption of the classical Black-Scholes model. The It^o's theorem was applied to the associated Stochastic Di�erential Equations (SDEs) for conversion to Partial Dif- ferential Equations (PDEs), while two approximate-analytical methods: the Modi�ed Di�erential Transformation Method (MDTM) and the He's Polynomials Technique (HPT) were applied to the Black-Scholes model for stock option valuation; in both cases the integer and time-fractional orders were considered, and the results obtained proved the latter as an extension of the former. In addition, a nonlinear option pric- ing model was obtained when the constant volatility assumption of the classical linear Black-Scholes option pricing model was relaxed through the inclusion of transaction cost (Bakstein and Howison model). Thereafter, this nonlinear option pricing model was extended to a time-fractional ordered form, and its approximate-analytical solu- tions were obtained via the proposed solution technique. For e�ciency and reliability of the method, two cases with �ve examples were considered: Case 1 with two ex- amples for time-integer order, and Case 2 with three examples for time-fractional order, and the results obtained show that the time-fractional order form generalises the time-integer order form. Thus, the Black-Scholes and the Bakstein and Howison models for stock option valuation were generalised and extended to time-fractional order, and analytical solutions of these generalised models were provided.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | Stock options, Stochastic di�erential equations, Option valuation, Ana- lytical solutions , Fractional calculus, Approximate-analytical methods. |
| Subjects: | Q Science > Q Science (General) Q Science > QA Mathematics |
| Divisions: | Faculty of Engineering, Science and Mathematics > School of Mathematics |
| Depositing User: | Mrs Hannah Akinwumi |
| Date Deposited: | 13 Dec 2017 08:00 |
| Last Modified: | 13 Dec 2017 08:00 |
| URI: | http://eprints.covenantuniversity.edu.ng/id/eprint/9798 |
Actions (login required)
 |
View Item |
