Browsing by Author "Premarathna, L.P.N.D."

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Finite Difference Approximation for Valuation of Option Prices with Dividend Payments of the Underlying Assets
(University of Kelaniya, 2012) Premarathna, L.P.N.D.; Karunathilaka, N.G.A.
The development and the expansion of financial derivatives can be considered as the most significant events in finance during the past decade. The main purposes of the derivatives are hedging or providing risk reduction, arbitrage, and speculation. In the 1970s, Black, Scholes, and Merton developed the Black-Scholes partial differential equation considering the no-arbitrage principle for pricing financial derivatives. However, the efficient computation of prices and hedges for derivative products is a major concern for financial institutions since various assumptions and simplifications have to be made in order to obtain an analytical solution of the Black-Sholes equation. Hence, the resulting analytical solution does not reflect the reality. The remedy consists of discretization of the Black- Scholes equations using some numerical technique in order to obtain an approximate solution. Throughout this work, we present some Finite Difference Methods for solving the Black- Scholes model with dividend payments and discuss their convergence properties.
Tables for Testing Simultaneous Homogeneity against Ordered Alternatives in 3-Way Layout and Latin Square Design
(University of Kelaniya, 2008) Premarathna, L.P.N.D.; Kulatunga, D.D.S.
The likelihood ratio test for testing simultaneous homogeneity of main effects of several factors against ordered alternatives in multifactor designs has been developed in the literature. But the level probabilities needed to implement these tests have been computed only for the 2-way layout. We use these results to calculate critical points for testing simultaneous homogeneity of main effects against simple order alternatives in 3-way layout and Latin square design. Tabulation of critical values requires finding values of c that satisfy _2 m+n+t Pr(E (m,n,t);:::: c)= I Q(l;m,n,t)Pr(B1 1 ;:::: c), for 3-way layout and l=4 -(/-3) -(mnt-1+2) 2 ' 2 _2 3 m Pr(E (m,m,m);:::: c)= I Q(l;m,m,m)Pr(B1 1 2 ;:::: c), for Latin Square -(l-3) -(m -/+2) l=4 2 ' 2 -2 Design, where E is the corresponding likelihood ratio test statistic, Q(l;m, n,t) are convolution of probabilities used in order restricted inference and Ba,b is the Beta distribution with parameters a, b. The tables presented here provide critical values for testing at significance level a for the combinations of m,n,t and a, where m,n,t = 2(1)10, a= 0.1, 0.05, 0.025, 0.01, 0.005. An application in the case of Latin Square Design and FORTRAN programs for the computation of critical values in several layouts are also presented.
Valuation of options in Black-Scholes Model using finite difference methods
(University of Kelaniya, 2011) Premarathna, L.P.N.D.; Karunathilaka, N.G.A.
A benchmark mathematical model for the description of financial derivatives was introduced by Fischer Black and Myron Scholes in (1973, [1]) and equation was simplified further by introducing (Brennan and Swartz, 1978, [2]) and resulting equation is given by ( ) (1) where, : price of the underlying asset, : risk free interest rate, : the time, : volatility of the underlying asset, : price of the derivative In the absence of assumption free analytical method to obtaining the solution of the full model, various numerical algorithms are used. This work is mainly focused to analyze three finite difference methods namely Forward Time and Centred Difference (FTCS), Backward Time Centred Difference (BTCS) and Crank-Nicholson (CN) . It was found that both implicit FTCS and explicit BTCS and implicit CN schemes are consistent and explicit BTCS scheme is conditionally stable under (2) and both implicit FTCS and implicit CN schemes is unconditionally stable. Hence all the schemes are convergent in the view of Lax-Richtmayer equivalence theorem. Finally these algorithms are implemented using MATALB and the convergence properties of the schemes are shown by numerical experiments.