Page 45 - programme book

AM-010
Numerical Simulation of American Style of Asian Options under Jump
Diffusion Process

Mohamed Faris Laham 1, 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: mohdfaris@upm.edu.my
b) iqmal@upm.edu.my

Abstract. In today's financial markets, American style options are important derivative contracts. They
trade in large volumes on a variety of underlying assets, including stocks, indices, foreign exchange
rates, and futures. In this study we derive and analyze a penalty method for solving American style of
Asian option problems. A small non-linear penalty term is added in the Black-Scholes equation. We
remove the free and moving boundary imposed by the contract's early exercise feature to get a stable
solution domain in this approach. By including Jump-diffusion in the models, they are able to capture
the skewness and kurtosis features of return distributions often observed in several assets in the market.
The performance of the schemes is investigated through a series of numerical experiments.

Keywords: Option pricing, penalty method, Asian options, American-style Asian options.

AM-011
Valuation of Power Call Options PDE under the Black-Scholes Model

Nurul Nabilah Rozlin 1, b) and Siti Nur Iqmal Ibrahim 1, 2, a)

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: iqmal@upm.edu.my
b) nabilahnurul139@gmail.com

Abstract. The Black-Scholes model is associated with partial differential equations (PDE) and this
study aims to develop a pricing model for European power call options under the Black-Scholes model
using explicit, implicit, and Crank-Nicolson methods. These methods use the PDEs to numerically
approximate the option prices. Numerical results compare the accuracy and efficiency of the methods
for pricing options with nonlinear payoff.

Keywords: Power options, Black-Scholes model, partial differential equations

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