ANALYTICAL STUDY AND GENERALISATION OF SELECTED STOCK OPTION VALUATION MODELS

Simple item page
dc.creatorEdeki, S.O., Covenant University, Theses
dc.date2017-06
dc.date.accessioned2025-04-01T11:16:35Z
dc.descriptionIn 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.
dc.formatapplication/pdf
dc.identifierhttp://eprints.covenantuniversity.edu.ng/9798/
dc.identifier.urihttps://repository.covenantuniversity.edu.ng/handle/123456789/39047
dc.languageen
dc.subjectQ Science (General), QA Mathematics
dc.titleANALYTICAL STUDY AND GENERALISATION OF SELECTED STOCK OPTION VALUATION MODELS
dc.typeThesis

Files

Original bundle

Now showing 1 - 1 of 1
No Thumbnail Available
Name:
SO_EDEKI_PhD_2017.pdf
Size:
3.95 MB
Format:
Adobe Portable Document Format
Download

Collections

EPrint