Конференция, 2012, Проекти и региони
Permanent URI for this collectionhttp://research.bfu.bg:4000/handle/123456789/1793
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Item CLASSIFICATION AND IMPORTANCE OF BARRIER OPTIONS(Бургаски свободен университет, 2012) Milev, Mariyan; Petkova, MilenaIn the present paper we explore pricing of continuous and discrete barrier options that become more and more popular because of lower costs than their plain vanilla counterparts. We briefly describe different kinds of barrier options and their importance in Finance. Our financial analysis and the respective mathematical formulation give the possibility to be invented efficient computational methods for valuation of path-dependent derivatives that have not only a simpler computer implementation but also differ with minimum memory requirements and extreme short computational times.Item PRICING DIGITAL OPTIONS AND VALUATION OF THE GREEKS BY SPECIAL FULLY IMPLICIT SCHEMES(Бургаски свободен университет, 2012) Milev, Mariyan; Milev , NedelchoUsing classical finite difference schemes often generates numerical drawbacks such as spurious oscillations in the solution of the famous Black-Scholes partial differential equation. We analyze the fully implicit scheme, frequently used numerical method in Finance, that in presence of low volatility arises spurious oscillations. We propose a modification of this scheme so that we guarantee smooth numerical solution, free of spurious oscillations and satisfies the positivity requirement, as it is demanded for the financial solution of the Black-Scholes equation. The method is used, within the strategy suggested by Rannacher, only in few initial time steps in presence of discontinuous initial conditions. As a consequence, although the method is low order accurate, it returns a spurious oscillations free solution. Next, starting from the smooth initial condition obtained, any other family of arbitrary higher order schemes may be used.