Kesirli black scholes opsiyon fiyatlandırma yaklaşımlarının incelenmesi ve uygulamaları.

One of the fundamental research areas in the financial mathematics is option pricing. With the emergence of Black-Scholes model, the partial differential equations (PDE) for option pricing have started to be used widely. PDEs are adopted for both finding numerical and analytical solutions and developing new models for option pricing. One of the significant PDE is fractional Black-Scholes PDE. Essentially, a PDE can become non-local with fractionalization and this non-localization enables to expand the time frame of that equation. Several fractional Black Scholes equations are proposed in literature. The ones relevant to the topic of this thesis are summarized. The main contribution of this thesis is the development of new fractional Black-Scholes PDE through fractional heat equation and fractional Brownian motion. The new models are evaluated for particular cases and correspondence with Black Scholes PDE is noticed. Moreover, because the valuation of option is as necessary as the derivation of an option valuation model, the explicit method is expanded to a fractional explicit method. The new method is to find a numerical solution. The Fractional Black Scholes PDE is solved by the proposed fractional explicit method and the solutions are compared with the classical ones.M.S. - Master of Scienc