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Numerical Techniques to Solve Black- Scholes Equation

Thesis Info

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Author

Ashraf, Muhammad

Program

PhD

Institute

Riphah International University

City

Islamabad

Province

Islamabad

Country

Pakistan

Thesis Completing Year

2015

Thesis Completion Status

Completed

Subject

Natural Sciences

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/6883/1/Muhammad_Ashraf_Maths_RIU_2015.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726783732

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Black-Scholes equation is a revolutionary concept in the modern financial theory. Financial instruments such as stocks, commodities and derivatives can be evaluated using this model. Option valuation, a part of derivative products, is extremely important to trade in the stocks. The numerical solutions of Black-Scholes equations are used to simulate these options and are addressed in this dissertation. In particular, the discontinuities in the domain are addressed. The discontinuities in options create oscillations near exercise price in the solution. A grid adaptive finite difference technique is developed to evaluate financial options using Black-Scholes equation. The grid is refined near the exercise price to resolve discontinuities in the option evaluation and a coarse grid is generated otherwise. To cope with these uneven space steps, an innovative numerical finite difference schemes are developed named as adaptive explicit, adaptive fully implicit and adaptive Crank Nicolson techniques. These techniques are used to cure oscillations produced by discontinuities in the digital and butterfly options. These techniques are also used to simulate multi-asset digital and butterfly options. The numerical experiments show that the adaptive finite difference method is much more efficient than the method with uniform spacing. The technique reduces the points drastically which in turn decreases the computational cost and makes the algorithms highly efficient
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Suppressing the Level of Corruption in Kampar District: A Study of The Impact of Accountability, Audit Opinions, Publication of Financial Statements, Audit Results And Follow-Up Of Audit Results

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Role of Exopolysaccharide in Development of Biofilm and Antibiotic Resistance of Pseudomonas Aeruginosa Isolated from Infected Wounds

Nosocomial infections caused by multiple antibiotic resistant bacteria that are particularly difficult to cure, cause a considerable health risk and place an enormous burden on the economy. A primary reason of such nosocomial infections is the biofilm-forming Pseudomonas aeruginosa that primarily infects immunocompromised individuals and those with severe burn wounds. Inspite of P. aeruginosa being among the major cause of nosocomial infections, still little is known about the in vivo biofilm phenotype and the bacterial factors that prevent wound healing and promote persistence of P. aeruginosa at the site of infection. In the present study, P. aeruginosa isolates were collected from surgical wards of a tertiary care hospital of Pakistan Institute of Medical Sciences, Islamabad, Pakistan, from November 2007 to February 2009. 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