• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.22 no.1
• /
• pp.75-89
• /
• 2018

This paper presents the numerical valuation of the arithmetic Asian option by using the operator-splitting method (OSM). Since there is no closed-form solution for the arithmetic Asian option, finding a good numerical algorithm to value the arithmetic Asian option is important. In this paper, we focus on a two-dimensional PDE. The OSM is famous for dealing with plural-dimensional PDE using finite difference discretization. We provide a detailed numerical algorithm and compare results with MCS method to show the performance of the method.

• East Asian mathematical journal
• /
• v.35 no.1
• /
• pp.59-66
• /
• 2019

In this paper we study implicit-explicit (IMEX) methods combined with a semi-Lagrangian scheme to evaluate the prices of fixed strike arithmetic Asian options under jump-diffusion models. An Asian option is described by a two-dimensional partial integro-differential equation (PIDE) that has no diffusion term in the arithmetic average direction. The IMEX methods with the semi-Lagrangian scheme to solve the PIDE are discretized along characteristic curves and performed without any fixed point iteration techniques at each time step. We implement numerical simulations for the prices of a European fixed strike arithmetic Asian put option under the Merton model to demonstrate the second-order convergence rate.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.20 no.2
• /
• pp.123-135
• /
• 2016

This article deals with the pricing of Asian options under a constant elasticity of variance (CEV) model as well as a stochastic elasticity of variance (SEV) model. The CEV and SEV models are underlying asset price models proposed to overcome shortcomings of the constant volatility model. In particular, the SEV model is attractive because it can characterize the feature of volatility in risky situation such as the global financial crisis both quantitatively and qualitatively. We use an asymptotic expansion method to approximate the no-arbitrage price of an arithmetic average Asian option under both CEV and SEV models. Subsequently, the zero and non-zero constant leverage effects as well as stochastic leverage effects are compared with each other. Lastly, we investigate the SEV correction effects to the CEV model for the price of Asian options.

• Communications of the Korean Mathematical Society
• /
• v.28 no.2
• /
• pp.397-406
• /
• 2013

We present an improved binomial method for pricing European- and American-type Asian options based on the arithmetic average of the prices of the underlying asset. At each node of the tree we propose a simple algorithm to choose the representative averages among all the effective averages. Then the backward valuation process and the interpolation are performed to compute the price of the option. The simulation results for European and American Asian options show that the proposed method gives much more accurate price than other recent lattice methods with less computational effort.