Page 69 - programme book

OT-002
Numerical Approaches for Solving Mixed Volterra-Fredholm Fractional
Integro-Differential Equations

N.M.A. Nik Long 1, 2, a) and K. Alsadi 1, b)

1 Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia
2 Institute for Mathematical Research, Universiti Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.

a) Corresponding author: nmasri@upm.edu.my
b) GS58225@student.upm.edu.my

Abstract. In this paper, an approximate solution for solving nonlinear mixed Volterra-Fredholm
fractional integro-differential equations is presented. The fractional derivative is defined in terms of
Caputo type. Two methods are suggested: Adomin Decomposition Method (ADM) and Residual
Power Series Method (RPSM). In these methods, Adomian polynomials and residual function are
derived. The fractional Volterra-Fredholm integro-differential equation is reduced to a recurrence
formula, in which it can be solved rather straightforwardly. Numerical examples demonstrate the
efficiency and accuracy of ADM over RPSM.

Keywords: Fractional integro-diffferential equation, Caputo derivatives, Adomian polynomial
residual function.

OT-003
The Heston-CIR-Merton Model for Equity Warrant Valuation

Aisyah Syahirah Sawal 1, 2, a) and Siti Nur Iqmal Ibrahim 1,2, b)

1 Institute for Mathematical Research, Universiti Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.
2 Department of Mathematics, Faculty of Science, Universiti Putra Malaysia,
43400 UPM Serdang, Selangor, Malaysia.

a) Corresponding author: aisyahsyahirahsawal@gmail.com
b) iqmal@upm.edu.my

Abstract. Warrant is a derivative that gives the right, but not the obligation, to buy or sell a security
at a certain price before expiration. Warrant valuation method was inspired from option valuation
because of the similarities of these two derivatives. Nonetheless, call option pricing models such as
Black-Scholes were proven to contain many flaws, such as the assumption of constant interest rate and
stochastic volatility. The aim of this study is to develop a pricing formula for equity warrants which
includes stochastic volatility, stochastic interest rates and jumps. This dynamic is called the Heston-
CIR-Merton model. The development of the model involves the derivation of stochastics differential
equations which involves Cauchy problems and heat equations are then solved using partial differential
equations. The derivation of analytical solutions is also provided.

Keywords: equity warrant, Heston-CIR-Merton model, stochastic volatility, stochastics interest rate,
jumps.